I have been in America for two weeks = I arrived two weeks ago and I am still there.
I have been to America for two weeks = At some point in the past I visited America and I stayed there for two weeks.
We don't say "I've been there for two times". You can say "I've been there two times" but it's unnatural because we say "twice", not "two times". For more than twice, you can use the number (I've been there three/four/ten/a hundred times".