Yes, both of those are very correct. They could both be used naturally in conversation.

Best wishes is the most natural, informal ending to a letter from your list.

"What do you do to learn it?" is the more natural way of saying this.

"I have an unusual request from you." - Instead of saying from you, say for you. "I have an unusual request for you.". This is more natural. "I have an unusual request to ask you." is very natural sounding! Good job! "I have an usual request to make to you." - Though this is grammatically correct, the "to you" part is unneeded and unnatural sounding. Just saying, "I have an unusual request to make." sounds more natural and conveys your idea. :)

No. This sentence makes sense, and it translates your idea, however, this would not be said. A better way to phrase this would be to simply say, "Even adults should get new knowledge.". The part about children is implied with this sentence. Or you could even say, "Adults should get new knowledge as well as children.". And just a suggestion, even though it is grammatically correct, "get new knowledge" is not commonly said by native speakers. A more "fluent" way to say this would be to simply say learn. :)