No, you can't change the quality of artifacts. Those are set when you acquire the artifact. If you level one artifact up quite a ways, then fuse it into another, you keep all of the points, though. For example, if you have a level 12 red buddha statue and later get a purple buddha statue and fuse the former into the latter, the latter will immediately be at least level 12.
There are both daily world bosses at 8 pm EDT and daimyo world bosses at times set by the daimyo. It sounds like you miss both, which is unfortunate. That is a major disadvantage for you.