Can a US citizen working abroad for a foreign company contribute to a
Roth IRA and what are the limits?
Assume the citizen meets all requirements to be considered a foregn
resident by the IRS.

I lived in Germany for four years (2001 to 2005) and contributed to my
Roth IRA every year.  My pay was deposited into a US bank account, I
was paid in US dollars and I DID pay US income tax every year.  You
are required to to have W2 reported income equal to or greater than
the amount you deposit in your Roth IRA ($4000 per person per year
right now).  If you are trying to get out of US taxes and still
contribute to your IRA it may be trickier.

Good luck!