Repairing above-ground gaps and holes in foundation
Ultimately, I used two different types of cement for these two issues.
For the narrow gap, I used Quikrete Mortar Repair No. 8620-09, since it is advertised as a tuck-point compound. This is a light acrylic foam that hardens into a mortar-like substance. The applicator was able to inject the compound into the crack pretty easily.

For the larger hole in the concrete block, I use Quikrete Hydraulic Water-Stop Cement.

I had never used either of these before, but the instructions were easy to follow, and I was pleased with the results. The Quickrete cement dries quickly (5 minutes) so I had to work fast when using it.