How does the back part of the air cleaner housing come off on 99 dyna super sport.

You have something assembled wrongly. Get a local mechanic to have a look see.

Printed on side of tire in small letters

You may have too much oil in the system OR you may have a problem with worn/leaky compression rings OR the breather system may be plugged up in the rocker boxes OR the air filter may be plugged. There could be other problems but they would be hard to diagnose without having the bike for testing etc. Check the air cleaner first, then do a hot compression test and then a cylinder leak down test which will only diagnose the rings and top[ of the cylibder etc and will not show any cylinder damage below TDC

To remove a carburetor, first turn the fuel petcock off if it has an "off" positon. Then take the air cleaner cover, air filter, and air cleaner backing plate off. Loosen the adjustment on the throttle and idle cables (the two cables). Loosen the nut on the enricher cable and allow it to come out of it's bracket. Disconnect the fuel line and the vacuum line for the VOES and the petcock. Now, rock the carb side to side and pull it out of the carburetor intake seal and guide the enricher cable out. When you replace the carb, always use a new carburetor intake seal to prevent vacuum leaks.

Good Luck
Steve

it will either have a cable from back of odometer to front wheel or a speed censor on the wheel

Check to see if they both have the same diameter axle. Harley went from a 7/8 inch diameter axle to a 1 inch diameter axle sometime around that time period.

if it is fuel injected look for fuel pump impact senser and reset.