Congrats on finding and fixing the problem. That stream looks like an 18 year old. Next time lube the shaft and pump housing and impellor with dish soap and a little water. Yes the water is suppose to shoot from the hole in front.
Do you have any information on the make and model of the trolling motor? Does the motor plug also have four leads? Measure where there's voltage and ground on the socket then replace both socket and plug. Knowing where the ground and voltage are on the existing socket will give you a head start...
Whats condition is the fuel primer bulb in when the motor bogs down? Is it firm or are you able to squeeze it? Is the fuel tank vent clear? Anyway to tempy run the motor on a portable tank?
Can you post a picture of the water pump housing part and seal that you're referring to that's missing. Also as 99yam40 said, make sure the water in the tank is above the level of the water pump not just the intake. Does any water come out of the pisser when you have the hose connected to the...
I'm guessing there is one common wire that goes from the ignition switch to each gauge. See if there is one wire that does that clip onto it then put the key switch thru each position and see what you measure, if anything.
You said you "got" the boat, did he dump it on you, give it to you or did you buy it? There's no registraion sticker on it either. What paperwork did he have on it and the trailer? Bill of sale means nothing how about pink slip and registration?