What are my chances of getting Airborne school if I go to Fort Bragg?

So long as you have a GT Score over 110, you can go to a USASOC unit. If you end up there you'll go for sure. Your odds of ending up in one of the 82nd BCTs are much lower because the quantity of units on Bragg requiring mechanics are high. Your better off following everyone's advice and get yourself pinpointed to USASOC. They can only tell you no.

The Army is not going to send you to a school like Airborne unless you need it to do your job. You want a shot a jump school, get yourself assigned to a slot that needs jump qualification.

100%. You do not want to be a leg.

It's easier to get at Fort Bragg. When do you get to Bragg? Are you going to an airborne unit? If so, contact your gaining unit and request it enroute. Otherwise, once you get there look for slots in an airborne unit and see if your command will do a 4187 for a cross-post transfer to an airborne slot. You can also do a 4187 to request Airborne school once you get there, if you're not in an airborne unit. It's something you need to talk to your new command about, since you'll need their support either way.

You tagged 82 ABN so if 82 ABN it is highest than most places in the Army. It all depends which unit and if it is a coded slot.

About 100%

Yes very dependent on your unit. Re-enlisting doesn't always work because many factors come in to play like MOS, strength for your rank across the army and class availability