well from the pump issue check the cover on chamber two over the bioballs, i had the same problem and it was because my water was too low then the cover wasnt letting enough water from chamber 1 get in to keep the water in chamber 3 high enough to keep it from bubbling.
the fan is a problem ive had a month since i got mine, very annoying. what ive found it to be is somehow the fans cooling the lights are rubbing against/vibrating off of something, remove the plastic cover of the lights, then the larger piece of metal from the bottom area and mess with the fans a bit until theyll quiet down, ive had to make mine so that theyre on all the time or else if they shut off when they come on theyll buzz again.
the green moss is diatoms/algae and is a sign that your cycle is ending, which is a good thing since now those damsels can be healthy, you should have read up on fishless cycling before this adventure, i know i wish i had
sterilizers i know nothing about so someone else will help but purple i woulsnt recommend, its useless and youll grow plenty of coraline on your own, i know i have!
as for upgrading unless you want to tear down your tank now i wouldnt suggest it, taking out all those bioballs will rid you of good bacteria that clean your tank up, ive read besides a bit of higher nitrates theres no difference and water changes can keep that down along with the skimmer you have. chaeto i have no clue about either
i own a biocube 14 myself and its great, hope you have as much fun as im having!