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.
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.