Learn French: J'écrirai l'introduction et la bibliographie d'ici demain. - I will write the introduction and the bibliography by tomorrow.

Avant just means "before," focusing only on the deadline. D'ici literally means "from here." Using d'ici demain emphasizes the whole block of time between right now and tomorrow, meaning the writing will happen at some point during this window.

Is it also correct to say d'ici à demain?

Yes! When followed by a time adverb like demain, tard, or ce soir, the preposition à is completely optional. Both d'ici demain and d'ici à demain are perfectly natural and mean the exact same thing.

Why do we need the article la before bibliographie when English just says "the introduction and bibliography"?

In French, articles must be repeated before every noun in a list. You cannot drop the second article to group them, so both l'introduction and la bibliographie need their own definite article.

Does using the simple future (j'écrirai) change the meaning compared to the near future (je vais écrire)?

Not significantly in this context. Je vais écrire can sound like a more immediate, concrete plan, while j'écrirai is slightly more formal. However, because you have set a clear deadline (d'ici demain), both tenses work perfectly to state your intention.