Shake the whole thing on the trailer, if there is water in a log you'll hear it. If there is water in the logs look to the back of the log where it is welded to the M brackets for cracks, that is the most common place for them. If you don't have drain plugs you'll have to drill some holes in the lower rear to drain the log. I drilled mine the size to tap a 3/8 pipe thread and then tapped the holes and just ran plastic pipe plugs back in and ran that way for over a year with no problems, so you can get them drained and plugged back up without a great big welding operation. Pipe taps are tapered so you only run the tap in about 3/8 of an inch to get enough thread to let the tapered plug seal. The plastic plugs on the top are vents. I did my work on a 1998 Fisher 20 so the boats are probably very similar. BTW those boats were known to leak at that weld and I know of two that were repaired under warranty to fix the leak, it is not a difficult or extremely expensive weld job, Any competent weld shop or backyard aluminum welder should be able to fix you up with the repair and the plugs, notice I said COMPETENT welder. I personally would get the water out and the motor running and check out the deck before I worried about fixing the leak. I drained mine after every trip like an old jon boat for more than a year before I got it fixed, never compromised performance noticeably or put us in any risk safety wise. Naturally you want to put the boat in the first time and run it a while then pull it out and drain it to see how much is getting in.
I think your kill switch is right above the lighter outlet to the left there a little. You can get the new tab to slide under with the coiled lanyard for it at walmart. That switch lets the power to the CDI bleed to ground so the motor will not run without the tab under it holding it open. You should be able to take the ignition switch out and get a key made, or maybe look closely at the switch face and the collar around the switch there may be a number there that you can take to a Mercury dealer, or locksmith and get a key made. You can also just buy a new switch for not a ton of $$, make sure you get a push to choke switch if that's what yours is.
This looks like a great candidate for a resto project to me, don't rip and tear at stuff, every issue you have mentioned is easily addressed, ask questions and we'll walk you through it.
Do not just start swapping out parts, you probably don't need coils, you need to get the kill switch open. If you crossed some wires under the hood and got it to crank without making spark it did that because the kill circuit is grounded out , it is exactly the same as the switch being in the off position, which it is, which also won't let it fire.
Turning the ignition switch on may power the accessories but it does not power the ignition circuit. It actually ungrounds the CDI box to allow the current created in the stator to power the CDI box. You don't need power to this motor to do anything except turn the starter, the stator makes the current to power the CDI which powers the coils and fires the motor, your's probably will run if you get the ignition switch out of the off position and open the kill switch circuit. Don't open the coils packages, you can send them back.
There are things that need to be checked on this motor before you try to run it, you should read the posts on "awakening a sleeping outboard"
If you get overwhelmed by this old girl and decide to bail out on it let me know in a PM, I might be a buyer. I hope you don't give up though, it is an easy fixer.