Hi mibato, the backfiring when downshifting could be due to a very lean fuel mixture causing detonation (check that the spark plug electrodes aren't white). Backfiring when downshifting can also occur if the ignition timing is off. What I would do is clean the carburetor while it's disassembled, replacing the gaskets and adjusting the float level if necessary. The float bowl might be dirty, which could explain the rough idle, or it could be due to a clogged jet or an air leak around the cover gasket. Also, check the vacuum lines going to the actuators for cracks or air leaks. In short, it's best to thoroughly inspect it while cleaning it (this kind of work shouldn't be done halfway with just a carburetor cleaner spray).