Before getting into the specifics of Puranic stories of Ganesha and its symbolic significance, it will be useful to understand the context of Puranic stories and their relevance in one's life.
Sri Chandrasekara Saraswathi in his book "Hindu Dharma" says the following.
In page 58 - 59 he describes Hindu Puranas and rituals as follows.
"Religious and philosophical truths are often explained through parables, stories, so that ignorant people can understand them easily. Since metaphysical concepts are difficult to grasp, either they have to be told in the form of a story or they have to be given the form of a ritual that is they must find expression as religious acts. For the common people the performance of a rite is a means of finding the truth present in it in the form of a symbol.
I do not, however, agree with the view that all rituals are nothing but symbolic in their significance and that there is no need to perform them so long as their inner meaning is understood. Ritual as ritual has its own place and efficacy. Similarly, I would not say that stories from the Puranas are nothing but illustrations or explanations of certain truths or doctrines. As stories they are of a high order and I believe that they really happened.
But, at the same time, they demonstrate the meaning of certain truths. As for rites, their performance brings up benefits. But in due course, as we learn to appreciate their inner meaning we shall become purified in mind. This is the stage when we shall no more yearn for any benefits from their performance and will be rewarded with supreme well-being (that is, liberation).
It is likely, though, that, with the passage of time, some stories or rites will become far removed from their inner meaning. Or, it may be, the inner meaning will be altogether forgotten. "
Puranas are NOT history documents and it is up to an individuals to believe them or not believe them . Regardless, the underlying metaphysical concepts , if shown to be represented by a given Puranic story, could be of value to a person.
In talking to a young adult, the key thing to emphasize is exhibition of mutual respect towards others. This means not to pass judgment on a believer or non-believer of such Puranic stories (which has useful metaphysical content).
However Puranas have evolved over a period of time and some may have lost the underlying significance.
In terms of the origin and birth of Ganesha there are many stories that is available today. There are also many vintages of these stories that are often modified/corrupted/embellished versions of the original stories.
The many stories about Ganesha are documented in this Wikipedia article.
https://en.wikipedia.org/wiki/Mythological_anecdotes_of_Ganesha
Let us take the well-known story and examine the significance. From the above reference, let me copy and paste the specific story for understanding the possible significance. This will address questions 1, 4, 5 from post 1 and also one of the questions from Post 2.
"The most well-known story is probably the one taken from the Shiva Purana. One day Goddess Parvati was at home on Mt.Kailash preparing for a bath. As she didn’t want to be disturbed, she told Nandi, her husband Shiva’s Bull, to guard the door and let no one pass. Nandi faithfully took his post, intending to carry out Parvati’s wishes. But, when Shiva came home and naturally wanted to come inside, Nandi had to let him pass, being loyal first to Shiva. Parvati was angry at this slight, but even more than this, at the fact that she had no one as loyal to Herself as Nandi was to Shiva. So, taking the turmeric paste (for bathing) from her body and breathing life into it, she created Ganesha, declaring him to be her own loyal son.
The next time Parvati wished to bathe, she posted Ganesha on guard duty at the door. In due course, Shiva came home, only to find this strange boy telling him he couldn’t enter his own house! Furious, Shiva ordered his army to destroy the boy, but they all failed.
This surprised Shiva. Seeing that this was no ordinary boy, the usually peaceful Shiva decided he would have to fight him, and in his divine fury severed Ganesha’s head, killing him instantly. When Parvati learned of this, she was so enraged and insulted that she decided to destroy the entire Creation. At her call, she summoned all of her ferocious multi-armed forms, the Yoginis arose from her body and threatened to destroy all. Lord Brahma, being the Creator, naturally had his issues with this, and pleaded that she reconsider her drastic plan. She said she would, but only if two conditions were met: one, that Ganesha be brought back to life, and two, that he be forever worshipped before all the other gods.
Shiva, having cooled down by this time, agreed to Parvati’s conditions. He sent Brahma out with orders to bring back the head of the first creature he crosses that is lying with its head facing North. Brahma soon returned with the head of a strong and powerful elephant, which Shiva placed onto Ganesha’s body. Breathing new life into him, he declared Ganesha to be his own son as well, and gave him the status of being foremost among the gods, and leader of all the ganas (classes of beings), Ganapati."
For a rational person, especially a young adult, the story seems strange at many levels. Let us list a few items
1. Why should goddess take a bath since they are supposed to be pure all the time.
2. Why should Nandi let Shiva pass?
3. Upon return of Shiva, why did this boy keep on fighting Shiva and not recognize him to be God?
4. Instead of fighting Shiva, why did Parvathi want to destroy the whole creation?
5. Why should Ganapathi be worshipped first?
6. Why pick an elephant's head to put on a boy?
I am sure there are many more such questions. Before answering them as to their possible meta-physical significance, it may be useful to understand a few unique and profound aspects of Hinduism. Their connection to stories such as this may be made later.
Today's adults and children born with a label Hindu are confused as to their identity. Hinduism is hard to define but there are few doctrinal aspects which is universal in its appeal. It is useful for young adult to appreciate the universal aspects of Hinduism symbolized in rituals and Puranas.
At the conclusion of this thread I will try to summarize all such aspects that were brought out in this thread. Here let us focus on few of the seminal metaphysical ideas as it relates to this Puranic story.
1. Hinduism is unique in the sense that it recognizes that the truth is understood by realizing both the male (Purusha) and female (Prakruthi) principles of Isvara. Most religions have completely ignored the female principle altogether. While Brahman is postulated as the cause of all that exists, it is impersonal and grammatically is neutral gender in Sanskrit. It is beyond the scope of this thread to go in depth about all these terms. The key point is that all worship of Isvara in Hinduism includes both male and female aspects. Prakruthi is synonymous with Nature which includes all that we see - power, wealth and knowledge. Our very body and mind is part of this nature.
2. Nature includes opposing attributes which our mind may terms as 'good' and 'bad', likes and dislikes etc. There is no concept of Evil/Devil at the most basic aspect of *understanding* Hinduism.
3. Purusha is the one that reveals all that exists in Nature. Our mind being part of nature *cannot understand presence of Isvara and understand all about Isvara* if it is masked by 'impurity' (which is part of nature also). Impurity includes pride, jealousy, wanting to do harm, wanting to cheat others etc. This is just a representative sample.
4. Our survival in the world depends on our sense of self identity which is often translated as ego (though there are better ways to express this). However this sense of self identity is the one that prevents us from recognizing the presence of Isvara.
5. If this ego is subdued all that exists is only Isvara that is recognized, ego being subsumed by Isvara for a lack of better expression.
6. To subdue this ego one needs enormous wisdom.
7. Hinduism does not have Gregorian linear time scale. It has cyclical time scale with things repeating - creation and dissolution in an endless cycle
Now let us see how this story can be related to these metaphysical ideas.
1. Goddess Parvathi representing Prakruthi/Nature taking a bath is like a person removing mental impurities such as the one described above. There are Nithya Karmas (daily activities) that can help remove the impurities of the mind. Nithya Karmas are discussed in another thread
2. When the impurities are removed, Isvara's presence is understood which is like Siva walking into the house without any impediment.
3. Nandi in the story is representative of the right attitude which allows Isvara to be recognized.
4. Ganesa as created by Goddess Parvathi from turmeric is like a person in this creation who has ego (sense of individuality) like you or I and therefore cannot recognize the presence of Isvara (Siva). He fights with all his might and does not recognize presence of Isvara.
5. When the ego is cut off (or rather the sense of individuality is cut off ) all that remains is Isvara in the absence of ego. Siva cutting off head of Ganapathi is like cutting off the ego at which point the appearance of creation ceases to exist (which is the result symbolized by Goddess Parvathi as Nature ceasing appearance of this universe and going into dissolution)
6. In the endless cycle, from dissolution to creation, Ganesha is given a head of elephant which represents enormous wisdom required to understand the presence of Isvara (Siva)
7. Ganas or class of beings represent all that is in this creation on which we are interdependent. Our existence and growth is only possible because of large number of natural entities that includes all beings. We survive our way though many impediments in nature using nature. By considering Ganesha as the presiding deity of all Ganas, we express our gratitude for all that has contributed to our wellbeing by worshipping Ganesha
There could be other interpretations but there is seemingly some connection between Puranic story and doctrinal thoughts in Hinduism
In the next post I will go into the worship of Ganesha to remove obstacles. What many may not know is that the 108 names of Ganesha that occurs in Archana includes the following one after another
1. My salutations to one that removes the obstacles in my life
2. My salutations to one that puts the obstacles in my life
So Lord Ganesha is the one puts the obstacles and creates problems? We will examine the profundity of this thinking, again unique to Hinduism in the next several posts.