Fix the caliper, that is going to cause you to wreck if it melts the brake line and bleeds all your fluid out. The ABS light is just a bad sensor most likely which is easy to replace and will not cause any issues besides the ABS will not work.
Traction control not working is kind of a bonus IMO... means if you forget to turn it off it doesn't surprise you.
edit: That caliper needs to get fixed like... yesterday btw, that is a legit safety issue and I'm not saying this to be an ***. It could be as simple as a stuck slide pin on the caliper which you can just pull out and grease up and re-install but if you've been smelling that burning and the caliper is sticking you likely have messed up the rotor and pad and need that replaced which means its time to do both sides and grease all your slide pins including the rears.
I use the purple advance auto lithium grease for $4. Bought it years ago and I've done a bunch of brake jobs and 3 transmission installs and its still like 3/4 full.
2000 Mustang GT Steeda build #48. Bolt ons, suspension, Novi 2000.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.