salt will dissolve very quickly.. the hard white residue after a good rinse is generally calcium/carbonate build-up... White vinegar and a razor blade will get the job done removeing it if it's needed/for astetic issues. I've never had a problem with it effecting my water dramatically. over time in softer water it will dissintigrate and harden your water slightly.. but w/ regular water changes it's not a big deal for most fish. Once it's cleaned up, and you've checked all the mechanical stuff ( ie the pump itself, build-up should not be inside it. If there is... I would soak it in a 50/50 white vinger/water solution over-night). White vinegar works great on build-up and unless you're literally dumping it straight inot your tank traces will not harm your fish unlike other chemicals. But I don't bother with it if it's a very light coat, only when it's starting to actually build-up. I would split the bio-media in your other filter into the new one to get a "seed" going. this should help speed up your process and get the new filter running efficently. also leave the old filter running on the tank if you intend to run only the sump. Maintain water changes keeping the ammonia best you can under 4ppm and you should be good in approx 2 weeks.
If the coating is light, hook the sump up asap. The sooner you get it cycleing the sooner your water perameters will even out.