Yes, the US regionals are desperate... I work for one of them and we can't fill our classes. Pilot shortage is hitting us. Couple this with the very low salaries and something's gonna have to give.
Quality of training depends very much on which regional... CHQ is going to be getting rid of their CRJs and they never had the proper training facilities for them... in fact they were buying time from other regional sims in other locations. The regional I work for has one of the best training departments in the US hands down and has the reputation to support it. Still pays horribly... but it's a decent start having been a CFI for 2 years before that.
Requirements for working in the US... you're going to need a work visa or Green Card... however all that works, I'm not sure.
Either way, regionals are good experience but poor pay in typically expensive locations (I commute to save money but it's a big hassle)
Questions? PM me...