If the crew is dropped below half do they still take Rout tests as normal?
What scenario was you playing?
p88 Boarding Action ends when one crew has routed or wiped out.
P96 and 97 for Sail on Horizon and Dangerous Waters ends when one ship is at 33% hull points or an hour has elapsed and neither ship is below 33% it is a draw.
I sailed to within 2" of another ship. When I moved again there was no way to avoid it. Is this a ram or collision?
Well a Ram is on purpose, a collision is by mistake. in any case you would do the All hands Brace for Impact section on 45 and the Ramming chart on 46. In either case the ships hit and could take damage.
When a ram happens but you dont take any damage, doboth ships keep moving?
In theory yes, unless you intended to board them. Refer to page 47 on boarding.