Yes, you need one: an Urchin or Remora would probably serve a 35 fine: I just had to replace my Urchin because it couldn't handle a 52g.
You know when the wind gets up and the surf produces yellow foam along the ocean shore, and it's pretty nasty? That's where intense aeration causes protein compounds and some phosphate, etc, to precipitate out and get washed ashore. A protein skimmer operates much the same: like water jetting into a bucket, it produces a froth in which the spare proteins and wastes of your tank are precipitated out as yellow foam, which a skimmer collects into a cup so you can toss it: by then the yellow foam has collapsed down to a dark, stinking fluid. You don't want it in your tank for the health of your fish and corals. You can live without a UV filter [a light that kills small animacules in your water] and you can live without a chiller, more than likely---a fan blowing over your open sump [you don't use lids in reefs] will serve that purpose, by heavy evaporation. You don't need a filter---shouldn't use one, because the rock and sand serve that purpose, and the cycles of a filter only impede their work and build up nitrate. But a skimmer is a good thing. An Urchin is in-sump, a Remora is HOB [hang-on]. They'll do what you'd wish your filter will do and won't. HTH.
