This may be a good way of invalidating your home insurance, if there were any issues. If it's visible, it may also get picked up by a Home Inspector, impacting resale.

I'll DIY lots of things, but gas isn't something I DIY.

I'd put a small bead of foam in the gap and then install baseboard.

I don't think the Sikhs would agree with this.

Can you unscrew the stopper? If they can't be taken apart under the sink, they normally unscrew or there's a small set screw somewhere.

Otherwise, you can buy plastic drain clog removers that get into tight spaces. Girls with long hair keep these things busy.

Have you tried a 5" wide heavy duty floor scraper? You can soak the glue in hot water. It's still a workout, but it should come up. I had to remove a vinyl floor from concrete like this in a bathroom.

What's the height differential between the garden surface and the garage floor? Acco drains will intercept surface water, but not groundwater. If you removed the drains, the soil underneath is still wet. The weight of this wet soil creates hydrostatic pressure which squeezes the water into nearby structures. Any crack is an easy path for water ingress, but concrete itself is porous so a couple of feet of wet soil will create enough pressure to cause penetration.

Did you install sill plate gasket under the framing's bottom plate?