Are you trying to restore the bike with all-original parts, or do you just want a functional speedometer/tach? If you're just looking for a speedometer/tach, then get a cheap bicycle tach with a magnet you stick on a spoke.

Is there a shutoff for the water supply? What if you shut it? Either the tank will eventually drain (flapper leak), or the tank will remain full (problem like over-fill). Check the max water level is usually imprinted on the tank, or the styrofoam insulation.

If you made the mistake of greasing the tracks....grease gets really thick in cold weather. This will confuse the opener into thinking it's hit an obstacle. The tracks need to be clean/dry.

Don't cover the drain. You also can't have a hump in the subfloor under vinyl plank. The box usually says something like 1/8" dip or hump over 8' max. Else it pulls apart at the seams

Agree. After sawing off the old nosing, I'd probably get a really thin 1/4" (or less) sheet of nice plywood and glue/nail it to the riser of that top step before putting on your new bullnose. This will hide that ugly horizontal line left when you cut that nosing. Use something like polyurethane construction adhesive to stick it on, then use latex caulk around the sides and bottom to hide the gap.

You can probably run a splitter off this, then attach a reducer on one side...the tough part will be connecting the splitter coz you have so little clearance. The one I linked looks like the head on the female end rotates so it can be tightened (as opposed to this one with a fixed head, which requires rotating the whole thing). Make sure you use lead-free brass.