Getting a private is hardly recreational study - it is full time, well over 18 hours a week - most of our students study 12-15 hours a day.
Yes but if you already have a EASA licence it should only require 5 or 6 hours including the flight test.....and this could easily be something which is incidental to the main purpose of your visit ie business or vacation...
After all, in the post-911 world, the US is more concerned with the training of pilots which is why the TSA undertake background checks....it is not about immigration law (which has not changed)