On contracts.
The contracts are not too complicated and there are only a handful of places giving them out that matter (RoH, NJPW, TNA, WWN/EVOLVE, CMLL, AAA, and other Japanese and Mexican promotions). While the contracts are all different, they're mostly the same in practice.
They work mostly the same as it WWE UK deals. WWE has priority on dates, and won't let them work for rival companies, but outside of that they are mostly free to do anything.
How it usually works is that a wrestler signs to a promotion and gives them priority on dates. Sometimes there is a limit on dates, essentially making them part-time deals, but others are almost full-time deals. Outside of these dates, guys are free to do shows for almost anyone else. Exact details vary.
There are usually some limits on guys, things like not appearing on TV or doing shows for rivals, not losing as a champion. Reasonable stuff like that. Some times they are more limiting (like NJPW having exclusivity in Japan), but they're rarely tyrannical.
The bit were it gets a little complicated is the RoH/NJPW agreement. This is basically a talent exchange deal where some NJPW guys will do RoH runs or RoH guys do tours in Japan. They also do joint shows. There are agreements with RevPro(UK) and CMLL (Mexico) that are more or less the same too.
The second complicated bit comes when guys sign with multiple companies, usually part time with both. A couple of examples are Scurll and Ospreay being signed to both RoH and NJPW, and Sabre Jr. being signed to WWN/EVOLVE and NJPW.
These deals are often worked out case by case, or negotiated in tandem to make sure they can work without issues. They're not really complicated, it's just the same as normal but twice. Guys who have these often are not big players for either promotion, but are stars who travel all over, the UK guys being good examples.
The last complicated bit is the free agents super stars. These are rare, but they sometimes happen. Cody is the recent example, working for RoH, TNA, and NJPW at the same time after he left WWE but unsigned to any of them. He eventually signed with RoH, but continues to do NJPW dates in a prominent spot.