cr500_af;659258 wrote: You'll be fine for a while, you just have to do water changes on schedule as you aren't removing stuff. Skimmerless tanks can work long-term; they just don't put up with slacking.
As for the pump, sometimes a cleaning will do it. I'd soak it in a vinegar solution. Once you get it to start, run it for a bit in the vinegar and then rinse well.