입다 is for shirts and such, 차다 seems to be for things you wrap around you, like watches or handcuffs.

No you can't say like that, with 허리띠, 귀걸이 and 목걸이 you must use 차다

~고 있다 makes it present progressive. (~ing)

It is one of the translations, yes. But check the comments above to understand what it means here.