...the thru hull valves in the head, one for the sink and the other is for what?
That depends on its size...a 3/4" (hose sizes are always stated as their INNER diameter) would be the flush water intake for the toilet. First thing you need to do is trace the routes of every hose on your boat to find out what each is connected to at both ends...'cuz when you find yourself stepping into water over your shoes is NOT the time to START trying figure out which one is the source of the leak!
Should they remain open at all times at the dock and closed underway?
Again, that depends on what they're connected to.
does the galley sink drain into the holding tank...
Unless for some reason the PO rerouted the sink drain line to drain into the holding tank (there are a couple of lakes in CA that have started requiring gray water holding), all sinks should be plumbed to drain directly overboard.
that the valve under the sink in the galley can be closed and the water will go out, is that correct?
That valve under the sink is most likely the seacock on your sink drain thru-hull...close it and the sink won't drain at all! If it's not a seacock, post a photo of it so we can see just what kind of valve it is.
...because holding tank fills up quickly with just the two of us on board.
Let's do a little math to see whether it's filling up faster than it should: The average adult uses the toilet 5x/24 hrs...avg flush: .6 gals (2 liters)...so that would put an avg of 3 gal/person/day into the tank...6 gal/day for the two of you. Divide the size of your holding tank by 6 to find out many days it should last you. Do some research in the sanitation and plumbing forum for tips on how to "stretch" holding tank capacity.
I suggest you spend a day going over every inch of your "new" boat to find out exactly what you have--and exactly where things are...what's connected to what else, what you really need to get the owners manual for (most are available from mfrs' websites) to learn how it works and--more importantly, how to maintain it. You're bound to have dockmates who are familiar with most of the systems on any boat...get to know your dockmates! Most people would much rather answer questions and help a newbie sort things out than start a pool to see who gets closest to the day and hour your boat sinks or hold their breath wondering whether you're about to blow up the dock .
And you'll always get answers to your questions here...a few of which might even be the right answers!