Does 'make sure' in the sentence mean 'do something in order to be certain that something else happens'? If it is, I want to make sure that you have fun. 너를 즐겁게 해주고 싶어. (I want to make you feel fun.) 너와 즐거운 시간을 보내고 싶어. (I want to have a pleasant time with you.)

I think yours is quite enough, but I'd say.."재미있게 (잘)지내나 해서" or "재미있게 보내는지 알아보려고" ^________^

There's always various expression under similar circumstance. again, it all depends on what you are saying to who. if that is to say to your friends: 니가 잘 지네고(보내고) 있는지 알고 싶어( present). It that goes to an elderly, then whole expression become total different.

if i go just literally, i guess it would be something like 너 재미있게 보내는지 확인 하고싶어요 .... but is there a more idiomatic / friendly / natural way to say this...?