Are these sentences acceptable?

#1 Is acceptable, however not how you would typically pose that question.
substitute 'what' with 'that which' or even just 'that'
#2 is great
#3 just needs a bit of assistance....
"very danger"
Im thinking you are looking to make a greater statement since 'very' is an adverb used for emphasis. I would offer a suggestion "very great danger" or "very grave danger".

Im not an English expert and Im sure there are those who would make some other, perhaps more correct comments.

OristarA - may I ask what the intent of your sentence (1) is?

If you are asking if people might like to SUGGEST the names of books they have enjoyed, I would make it: "Who would like to make suggestions about books they have enjoyed here?" or "Who would like to recommend good books here?"

Re sentence (2) - what you have written is fine - but it does sound a little foreign to the English-speaking ear, which is absolutely fine. We MIGHT tend to say: "There was never such a cat!" - but i am nit-picking.

Re (3) - I would simply say: "You are about to place yourself in a position of great danger." If you want to make it even stronger, I would make it "extreme danger", or "grave danger" - however, all your sentences are quite comprehensible. I just am not really happy with the "very".

Regards,

deb