What you're describing could definitely be a compression issue. A quick and easy way to perform a compression check is to lift the saw off the floor by the starter handle. If it steadily drops, the compression is too low. Normally, it will drop a bit, then a marked pause, then drop a bit more.
If the compression is low, I'd probably toss the saw and get something better (Honestly, that's a pretty junky/cheap saw).
If it DOES have low compression, don't try messing with it trying to hone the cylinder, etc. For one thing, there is no such thing as an oversize ring for it. Those cylinders are unplated (bare aluminum, easily scored). You're going to need a new piston & cylinder if you want to do it right. You actually don't HAVE to have any special tools, although they do make it easier. (There are no valves, btw). A piston & cylinder set will run you around $60.