I would be sure to use plastic shims on the floor, not wood. Use plenty, especially on corners (most important).

And, yes, drop the toe kick to the floor, just like you would do baseboard and shoe molding. Scribe it and trim it if there are gaps that the toe kick can't close.

There's a lot of videos on youtube to help.

Here's a link to get started on more directions.

https://youtu.be/-dFYUnSnKPs

"When I install the toe kick, can i just drop it to the floor to cover the shims?" Yes.

"What about mop water or spills seeping under the toe kick?"

Fugetaboudit.

"The blind corner back side is particularly out of level, it needed 4 shims. But, i figured since no one will be able to see the bsck once the countertop goes on, its ok??"

Yes.

I usually do eaxctly that and run a bead of clear silcone along the bottom of the kick just as and added precaution. Old houses are fun aren’t they. Those cabinets all need to be attached to the wall too BTW

We have a slope in our floors in our 1975 era colonial and our guys have used shims to make everything level. We actually had to order wider trim to drop to the floor because we needed over 4 inches in some sections. Did the same thing in our last kitchen and we never had any issues with spills etc.
Impressed that you are installing yourself. Good luck!

Scribe to the floor. A trim contractor can do that in an hour. Don't get this far and end with a hack job

Hi Jan, noted and considered, thanks!

How to install cabinet toe kick base on an unleveled floor

https://youtu.be/hKMrj-aW_4Q

Hopefully the scribe is thick enough to cover gaps. If you need more coverage in front of toekick for floor gaps, quarter round will work,too.