You can't use 'request' directly with 'you'. You need a preposition, so all of your examples are incorrect, sorry.
1. Can I request one thing of you?
2. I have one thing to request of you.
2. I'd like to request one thing from you.
3. I want to request one thing from you.
However, if your context is a child asking another child, 'request' is a little formal, so 'ask' might be more appropriate, but even then, this is a relatively formal and polite sentence structure for children to use.
I think that even better would be: "Please do one thing for me."