"I wonder if my HS 163FML 200cc engine is a pushrod type engine. It doesn't have any ports on the top of the engine for adjusting valve clearance"
It's a push rod engine based on the CG125 Honda engine.
http://hondacg125.awardspace.com/valve_clearance.htm

"I can't even get it to crank anymore."
Do you mean that the engine will not turn over when you push the starter button? Did you accidentally turn on the kill switch? What happens when you use the kick starter?