You don't need to convert your EASA licence to FAA. There's a procedure you have to go through that would allow you to obtain a temporary FAA licence which is based on your EASA licence.
You do not need any visa for hour building, if the immigration agents ask you what you are up to, just tell them that you coming for a vacation and a tour on your own in the States. Better not mention the verb "to fly" though.
A safety pilot doesn't imply you are enrolled in a course.