What/which more/better

Hello!
1. You want to use "which" when the choice is restricted: there are only four seasons, so it'll be "which". You used it perfectly well in your third question: which (among the 3 examples) is the correct reply.

2. I find the first sentence a bit awkward; I would expect something like "than anything in the world" after more. You can also say: I prefer tea to coffee.

3. Since the question is "when", you should answer "(it's) on June 23rd"
To me, answers 1 and 2 correspond to the question: "what's your mother's birthday?"

A simple 'June 23rd' works for me, but we must remember that this is a casual spoken dialogue, and it would be impossible to set any of your answers above the others in terms of 'correctness'-- they all work fine, as do 'the 23rd of June', 'the 23rd' (if it is currently June), etc.

"what" vs. "which" = 'identify" vs. 'choose'

No choice is implied. At least no context is given by which we might infer a choice, so by default the question asks us to identify something.

"What season do you like best?"

An addressee with an imaginative turn of mind will not be content with a restriction to the four standard seasons of the year. "I like income tax season best. I'm getting a big refund this year!" "I like early fall best, when the trees are just beginning to change colors." "I like the post-Christmas sales season at Macy's. Everything is marked down at least 50%."

Nevertheless, you won't be arrested and imprisoned for "Which season ...?"

I like "I like tea better than coffee" more than "I like tea more than coffee".

But I have to say "to like something better than ..." is strange, because the non-comparative form is strange: "to like something well" ?"I like tea well."

All "June 23" answers are correct. In informal conversation, I would use the first.

CJ