dropping the chain even after several readjustments sounds like the front derailleur just can't hold it's limits for whatever reason or the FD cage is bent... or maybe it just sucks, lol. Might have been able to just buy a new front derailleur to solve that I would think but I could be wrong.
As far as chainsuck, sometimes when a chain is brand new and not broken in, its a bit stiff but if it's still sticking even after breaking in, sometimes the factory grease on the chain is TOO damn heavy. My motobecane exhibited the same symptoms when I first got it... chainsuck galore. As an experiment, I threw the chain in acetone, rinsed, then simple green, rinsed, then denatured alcohol to get rid of all the thick factory grease (may have been overkill, lol) and then sprayed it down with triflow (a light teflon lubricant)... no more chainsuck.