Rhapis palms are a clustering palm that shoot vigorously and continuously. They are easy houseplants and are highly prized in East Asian countries (to which they are native). I summer all my palms outside but you do not have to--this species is particularly good indoors as it's one of the few species of palms that really needs to be protected from strong outdoor sun (or it'll burn). Indoors, it should be fine in a bright window with perhaps a light, shear curtain in hotter (southern or perhaps western exposures). They will also do fine in just bright light without any sun. I like to use a well drained soil with them but adding some sand to the mixat time of transplanting. They don't like getting too dry so watch the moisture levels. It's possible that the shoots with dry, dead leaves are already dead but they may not be. Cut off all dead leaves, leave the trunks and wait to see--if nothing develops after a few weeks, they're dead and may be removed. I feed every couple of weeks with a high nitrogen fertilizer. Once they start growing, you can easily propagate your pland by gently removing it from the pot and using a sharp, sterile knife to separate a shoot or shoots from the mother plant--they will be connected below the surface of the soil by roots--be sure to get shoots with at least some of their own roots already growing. They can be quite expensive--so it sounds like you made off with quite a deal!