1. If you did get European ratings and convert them to US licenses you could get hired to fly in the USA providing you got the coveted 'green card'.
2. Don't know. Seems possible, but I have never heard of anyone who has done it.
3. US flight schools are exactly that- flight schools. There are no educational prerequisites, no math classes. They teach nothing but flying. Your education is not their concern. If you are talking about getting your degree AND your licenses via an aviation university, this is something different.
4. There are several Flight Schools/Aviation Academys in the US whose sole business it is to make you a pilot. Depending on where you go, the cost for your Commercial/Multi/Instrument will vary from $30,000-$60,000 US. Some schools have agreements with regional airlines to get their students interviews upon completion of their program. Mind you- these interviews are are all with regional airlines. There is no such thing as a training program with a direct entry into the major airlines in the USA. These 'fast track' programs train a pilot from zero hours and offers a chance to be placed as a pilot with about 500 hours TT. This type of pilot is only considered at a regional, as regional minimums are usually 1,000 TT, but an exception is made for program pilots. You can find out more about fast track programs by visiting: Pan Am Academy.com
, The Airline Training Academy
, Airline Transport Professionals Inc.
& Mesa Airlines Pilot Development
There are lots of US flight schools that train foreign students and offer student visas & housing as well. These programs run about $20-30K US, but is not 'airline specialized training' and offers no chance at regional airline employemnt- just your licenses. You need to find a way to build your time to airline mins after that.