The black smoke indicates momentarily rich mixture during engine acceleration - nothing to worry about, but you should check your mixture adjustment. Run engine close to full speed, and adjust main mixture control (under floatbowl) richer and leaner to find rich and lean limits before it gets slightly rough, then put it halfway between. There is a separate idle mixture adjustment sticking up vertically from the top of the carburetor - adjust that one with the engine idling.
It should never blow blue smoke, regardless of what you do. Seems like your piston rings are past their best. You should think about replacing them - until you do, it will almost certainly have some blowby, which will sludge up the crankcase and cause some engine wear. It isn't an urgent issue, but if you end up with everything else working well, it seems worth getting the engine right as well.
