Hi Doug,
I don't know the Oysterman but it sounds like a pretty normal set up with thru hulls in the cockpit and hoses leading from those to thru hulls in the hull?
If so and the lower thru hulls are below the waterline then water would come up in the hoses to a point level with the actual waterline.
If the motor hasn't been run in a while and is a 2 stroke motor I would plan on having it serviced which would mean cleaning out the carb (old mixed gas will gum up the jets, float and filter) and rebuilding the water pump, check the plug, plug wire, etc.
If it has been run recently, check gas and open the tank vent on the cap, pump the (inline) primer bulb until firm, pull the choke out, advance the throttle about halfway and pull the cord (steady and to full length). When it fires, push the choke in some and the revs should increase. let it warm a minute or so then push the choke in all the way and reduce the revs.
Should be a little stream of water existing under the rear right side of the motor pan that lets you know the cooling system is working. You want to see a good solid stream, not spit and sputter or a weak stream. Sometimes salt builds up in the fitting the water comes out of so clean it out with a unbent paper clip or similar.
To shut down the motor, pull the deadman clip (red switch with a plastic circlip on lanyard) is so equipped and if not, pull the choke out.
In a lot of ways these small outboards are a lot like any other motor, if the plug is dirty or the fuel is bad they won't run.
6 hp is a good size but may not be enough if you have to fight current and/or tide.
Check out the centerboard before getting excited about it, might be in good shape. Once you get the motor sorted out you can anchor the boat in clean water, lower the keel and using a divers mask go take a look.
I goggled you boat, very nice! Lot's of good knowledgable people over on the trailer sailing and ask all sailor forums that will be happy to help.
Let me know if any of the above wasn't clear.
Good sailing and welcome aboard.
