Like others have mentioned to do, one of the very first things I do with a no-start is squirt carb clean into the carb and see if it'll fire. If it does, then that eliminates everything else, & I know to focus on a fuel issue.
If you indeed have a fuel problem, drain some off the bottom of the tank into a clear glass or clear plastic container and look for water or separated ethanol settled on the bottom. If you see any of that, dump that fuel, spray out the tank and line with carb or brake clean, throw a new fuel filter on there, and add fresh fuel. You'll probably want to disassemble and clean the carb, too.
If the starter struggles to get the engine past the compression stroke, a valve adjustment is needed. You should hear the starter load up while cranking the engine - just not excessively. Light loading suggests low compression that'll need to be investigated. Just listen to what the starter is telling you. If you suspect it's low, throw a compression or leakdown tester on and see what you've got.
I've used plenty of chinese carbs over the years. Most of them actually work pretty good. Just don't expect them to hold up to any kind of moisture in the bowl. Their metals SUCK. The carbs themselves are also hit or miss. I've had good luck with them over the years, but every now and then you'll get a bad one ... or a string of bad ones. Quality control is nonexistent ... but the same can be said for ANYTHING you buy today, cars & trucks included.