I made the same transition as you are thinking of, but it was 10 years ago so this info may wel be out of date.
The only thing that I was allowed to 'convert' was my UK CPL; I was granted a US CPL but with a big "PPL priveleges only" stamp
all over it. To get where I wanted to be I had to do the tests
theory and practical) for the CPL, IR, CFI and CFII. As some things are quite different "over there" I had to do some training before the tests.
As to visa, I went on an F1 student visa - to qualify for that I had to enrol as a student at a US university. You'll need to check out the visa situation with the US authorities - the US embassy web site used to be a good source of info.
Hope all this helps some - good luck!