my cousin has braces aswell and she has had those loose teeth aswell, dont worry kiddo, the root of the tooth is deep in there, braces will loosen your teeth, thats how they work, they pull teeth in which directon the orthodontist wants.
Did you get your braces tightened like 1-2 days ago? If so then the braces are doing their work, they are pulling the tooth. If you still feel uncomfortable call your doctor or go to his office and let him have a look
And the dental floss thread goes between my tooth and gum aswell, its normal because the tooth isnt attached to the gum around the edges much so dont worry about that
Best of luck