I live on the other side of Jamaica Bay, the Rockaways, and have a about 500 sf of raised decks on the east, north and south sides of my home. My decks are over sand, are not painted or stained - I just use a wood preserver. I don't know if the cleaning efforts are different with concrete underneath, but I finally found out something that works for me. My decks not only dry out, but accumulate algae in the shady areas which can get very slippery. For many years, prior to last year, I had rented a power washer and power washed the decks (heavy, wet, and pain in neck to drag back and forth to HD) or had used 'professional' services (expensive and not particularly good). Early last spring, I was both inspired and impatient and cleaned them myself with a a deckbrush on a stick and a bleach/water solution. I attached a deck scrubbrush to a stick (both available at hardware stores/HD, etc), and used a solution of about 1/3 of gallon jug of bleach to a bucket of water (I used the bucket that dry catfood comes in because it is square and doesn't narrow at the bottom). I was able to easily remove all the gunk and clean the deck....including those hard to reach corners, etc. There was no problem of the power washing blowing away bits of siding, etc. AND, I got some great exercise. The following day, I put on wood preserver. I can't remember which one, but it comes in 5 or 6 gallon can at HD. I do not use Thompsons because I find that in this beach environment, it makes the deck slippery when it gets damp - which is most mornings and evenings!
As to mosquitos......ughhh, just when the weather is great and the garden is in full glory...........zap. I hate them and have tried many things (plants, sprays, bug zappers, etc) over the past 40 years. I've won a few battles, but they have won the war. Goodluck.