The indirect object of request (you) usually takes the preposition 'of': may I request one thing of you? It sounds rather formal, I would generally use 'ask' instead - may I ask one thing of you? The 'of' is optional with 'ask', many people might say 'can I ask you one thing?'; similarly, all your alternatives work with 'ask'.

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."