The first one probably expresses your thought better, but it really is too absolute and will no doubt be argued by many. The best known saying in this sense is: ~Time heals all wounds. But you can find numerous articles and speeches that argue against it. I don't need to point out the kind pain from deeply personal losses that many people carry to their graves. Consider this Hebrew saying that is not quite as unequivocal: ~Time is a great healer. Anyway, here are a few other sayings you can ponder: ~Time destroys all things. (Dutch) ~Time heals old pain, while it creates new ones. (Hebrew) ~Time is anger's medicine. (German) ~Time works wonders. (Danish) ~Time, wine, women, and fortune, are ever changing. (German)

Just as you said in your explanation, "anything" works better than "everything". The first still seems a little awkward, logically, rather than grammatically. Time will fix everything. Time can fix anything. Just seem better. "can" seems rather non-specific about whether it WILL fix it, so everything seems wrong. "will" seems to imply that it WILL get fixed, so everything seems more appropriate. Anyway, the others have the answers.

the second one,it is more affin.

Aside from the philosophical arguments, the best way to express your thoughts should be: Time fixes anything.

the first one works for the situation you wish to express. the second one is ambiguous.