1. I think it comes down to preference, some like wet skimming some like dry. Maybe theres a benefit to either that I don't know about, so someone else can chime in there.
2. Yes
3. I wouldn't turn the skimmer off unless you're adding something to the tank that makes the skimmer go crazy and overflow, i.e. epoxy putty.
1) I typically find a happy medium. I like to make it a little more "wet" if i have to get organics out a little quicker. Also keep in mind aggressive wet skimming will affect your salinity level if left unatended.
2) 24/7 the only time i give my skimmer a rest is during a water change.
3)Dosing...well it depends on what your dosing. Try not to dose your tank right near an intake for obvious reasons. If you are dosing medications some will tell you not to skim others say it has no effect. So to answer your question no do not turn your skimmer off.
24/7 even if you are OVERSKIMMING, I'm runnig a Euroreef ES 52 w/ a mesh modded sedra 3500 pump on a 40 gallon breeder & 20 gallon long fuge/sump...........Rated roughly @ 150 gallons? But I do have a heavy biolaoad, my tank is stocked w/ many fish and frequent feedings!
Yes 24/7 most skimmers are "over zealous" their claims are always increased(gallon). But remember...a skimmer will skim if there is something to skim. :splitspin So don't worry. Take a look at the skim mate and this should tell the story. You will be fine running it 24/7