foreigners can definitely take the driving test here. you just have to have a Palau Social Security number. that means you also have to have a work permit in order to get the ssn.
the test itself is pretty straightforward. there is actually a handbook that you can review before taking the test and you can buy it for $5.
if i remember it correctly, the fee for the license is $25. you have to go set an appointment at the public safety office to take the written and actual driving exam.
hope this helps. good luck