It depends on the specialties involved but, in general terms:
1) If you're going to something that requires a separate intern year, like Anesthesia, Radiology, PM&R, etc - you can just get credit for the intern year you already did. That means you can apply to advanced+R spots, yes.
If you're going for a specialty/program that has an intern year built in, it's totally specialty dependent AND at the discretion of the new PD how much credit for prior training to give you. For example, psychiatry residencies have months of IM built in AND tons of elective time - switching IM->psych, the PD can easily request you get 12 months of credit for prior training, chop off some elective time, and let you start as PGY2 (or start as a PGY1 but advance you to PGY2 after a few actual psych rotations, then let you graduate early after 3 years total). On the other hand, switching into a surgical field, they'd be unlikely to give you any credit at all.
2) Funding is complicated, but in *general* terms, medicare funding is in two pots. Direct and Indirect Medical Education. When you "run out" of funding but are still training in a medicare funding spot, your funding from DME is reduced by 50%... but you still get the FULL amount of IME. The total proportion that is removed from the DME+IME pot really varies from region to region, but generally speaking, we're talking about no more than 20-35% total reduction. You're not exactly funded at a rate of zero.
But on top of that, *tons* of residencies have "unfunded" spots. Basically medicare froze funding at 1996 levels, so many programs that have grown since then have alternative sources of funding that they use for some of their residents, including internal money. This is totally irrelevant to most trainees, but what ends up happening is if you've "used up" your funding, some bureaucrat just says "you" are in an unfunded spot and trades it around. Program still gets the same amount of money regardless. Can every place do this? No. But most of the larger institutions can.
3) Anyone can try to do a second residency but you need to be relatively competitive for the field to start with - and have a damn good reason on why you're switching. Same as applying to anything else really.
