i wouldn't worry about the coil too much... it's basically all there still electrically. it's not unraveled or anything. maybe just hit it with a blob of silicone to keep it down and from flapping around. you absolutely will not find a new replacement for it...and if you did...buy a lottery ticket too. CRT parts are becoming unicorn poo.
the wire... if it is indeed connected to ground, you can just connect it to the metal frame on one of the screws.
the picture looks like it's missing green color? can you verify? it's probably either a loose wire connection...maybe broken trace or solder joint on the neck board or where the video goes into the board.