Many singers spend a lot of effort to sing graciously (or to improve/perfect their singing). but you make it look effortless/natural. Note: you can write the first part of the sentence many ways. Also, just because something looks effortless or natural does not mean that it is!

Squeeze is weird. "Many singers try so hard to get their best voice, but when you sing it looks effortless; you have a natural ability. ...or you could say, "you sing effortlessly'. You are using an adverb to modify singing and not an adjective because you are NOT modifying a noun. You are not modifying a person(noun) but rather an action(singing) done by the person. Good luck

You could say "at ease". The first part of the sentence sounds a little clumsy by the way.

No, you are quite right - a person can't be effortless. You could say: What you do appears/looks/seems/sounds effortless. Your singing appears/looks/seems/sounds effortless. You seems to sing effortlessly. And yes, 'squeeze' doesn't sound right here.