Unless your ambient RH is really low, there's no need for a dome. It's useful to delay that first (or '2nd') irrgation while the plants are sprouting, but once above ground, you don't want near-zero transpiration. That's great for cuttings but not seedlings.
Shouldn't have to spray it either. The moisture from the medium should be trapped and provide enough. A heat mat will definitely help if your air is cold. Get one with a soil thermostat - don't be cheap.
no picture so it's hard to say. if it's a round fuzzy white spot, that's really bad (mold is the devil!). If it's a hard water stain, that's nothing to be worried about.
If the plants are big enough go ahead and get the dwc going.. unless it's too difficult to move into a tent when it does arrive. Tents are nice but not necessary in vege phase. light pollution during dark cycle is mostly irrelevent. My vege tent is open 24/7 because i don't hook up an extractor or intake.. just a fairly strong clip fan blowing in that jostles the plants slightly while helping cool the light.
Is there a picture? i don't even see a diary. Another person seems to have access to a picture...