On the "jiggle the handle" problem, I had a neutral safety switch go out on my '86 MC PS190. Check that the 2 screws that hold down the two wires are on tight and not corroded. If the boat still has the problem, you can eliminate that switch be removing one of the wires and putting both wires on one screw, simulating the switch being on. If the problem goes away, replace the neutral safety switch.
The neutral safety switch is screwed into the top of your transmission, with two wires attached to the top. Should look like this:
http://www.skidim.com/prodinfo.asp?number=R153011 On your latest problem, it definitely sounds like a problem at your fuel filter assembly, or you kinked or plugged the line, or didn't reconnect something. The carb had some fuel left in it, so it burnt that up but then wasn't getting any more from your line. Take the fuel filter assembly apart again and check for things that would stop the fuel flow. Did you disconnect the fuel line from the tank or carb to clean another screen or filter? If so, check those too.