Hydraulic pressure from the pump at the front of the transmission is what engages the Forward or Reverse clutches.

If the pump isn't being turned by the engine, there's no pressure and the transmission is in neutral.

If you start the engine and now the pump is turning and producing pressure, you should be able to shift it into Forward or Reverse.

When you get it running, the shaft may spin slowly forward if you have excess drag in the forward clutches. You should be able to stop the shaft with a little pressure from a 2X4 against the transmission output coupling.

If you're putting it in gear on the trailer , the strut bearing in front of the prop should be lubricated to keep it from being worn by the shaft. Water sprayed in that area works real well since it's a water lubricated bearing that's always lubricated by the lake/river water when the boat is in the water being used

Some people will tell you that it needs to be immediately overhauled and some will tell you they've had that issue for years.

As long as it doesn't affect your low speed driveability it can be lived with for a long time. Sometimes a rebuilt transmission has this same issue when you get it back. Do a search for "dirty neutral" here on CCF for lots of reading

The transmission leak is probably the front seal and depending on the amount of leakage it could be lived with or replaced There's plenty of info on CCF about transmission leaks too.

The link below has info for Fantastic Finishes Marine and the new owner Joe who could answer whatever you might ask him

http://www.correctcraftfan.com/forum/forum_posts.asp?TID=47606&title=ffm-transmissions-has-moved" rel="nofollow - link

Impeller change is really worth the money, as an old one can break off pcs & clog the passages (esp. if run dry).  If that happens, the $50 or so would look like pretty small money.

Fuel in oil is probably a carb issue - how do the spark plugs look? 

Like SNobsessed said...............change the impeller, it's cheap, you have no idea what it looks like or how old it is and if the previous owner says it may need one, that's probably secret code for "I haven't looked at it for the last 10 years 

Before you get into the job, click on the link below to find lots of reading on how to make sure you get the pump reinstalled the right way 

http://www.google.com/search?q=https%3A%2F%2Fwww.correctcraftfan.+RWP+orientation&oq=https%3A%2F%2Fwww.correctcraftfan.+RWP+orientation&aqs=chrome..69i57j69i58.10515j0j4&sourceid=chrome&ie=UTF-8" rel="nofollow - link

As far as your carburetor, keep it simple and easy to understand, a marine one does a better job of making sure any overflow from the bowls ends up going down the carburetor throats and not spilling out onto the engine and hot exhaust manifolds. Gas and hot exhaust leads to fires and/or explosions.

Most all the "marine rated" stuff is there for that reason

Other things that are marine (or should be) for fire/explosion reasons  are

The carburetor

The fuel pump

The flame arrestor on top of the carburetor

The fuel lines

The alternator

The distributor

The starter,  With you having a reverse rotation engine, if you put an automotive starter on it, the engine would rotate the wrong way and never start anyways

Electric motors like the bilge blower are ignition protected

I'd get the boat running before you make any decisions on the engine, transmission etc. 1400 hours is not bad at all, depending on how it was taken care of for the last 40 or so years.

Oh and one other thing..............nice weather forecast for the next few days down there around Dallas assuming that's the one in Texas

Brave the intense cold by searching and reading a bunch here on CCF, indoors of course 

Are you sure its pushing water out the exhaust?  If you are running it with a garden hose stuck into the water intake, the water pressure could be pushing the water through and your pump is doing nothing.  Check that by pumping out of a bucket if that is not what you are already doing.