I don't think any of us should be trying to guess the color from this distance.
If the line between wall and countertop is narrow (and it usually is) sanded caulk may not be the best bet. The texture of the sand makes it hard to squeeze into the crack.
You can search Concrobium on this website. I know of at least one thread on the subject that has a recipe for a homemade Concrobium knock-off.
The fogger has the advantage of getting into hidden spaces.
True, chalk lines are almost useless. I did the same thing with a board and weights for hold-downs. I wouldn't walk backwards tho. the saw is designed to cut going forward.
And true, the asphalt could be deeper than than circ saw can cut, but as long as you have a clean cut at the surface...
You can get caulk in just about any color to match grout. Wherever two different surfaces meet, I prefer caulk. White vinegar and a stiff bristle brush should clean up the crack pretty well. Let it dry thoroughly before you fill it.
I've heard good things about the Concrobium fogger combination. It is supposed to actually kill mold spores. I don't think I would be too worried about staining as long as the mold spores are dead. No expert here, but the Shopvac plan sounds OK.
You'll want to use pretty long staples. I don't think a T-50 will do it.
Make sure to pay attention to the grain of the carpet. If you run your hand in both directions you'll see that the look changes. Try to arrange that the stairs will all lay the same way.
I would be checking with the local authorities and/or the water company. Ditto on the best possible pipe, you won't want to revisit this.
My first instinct was that the PVC sleeve sounded good. But if it ever leaks again, you will have a bear of a time trying to locate the leak
You don't have to do all the steps in a single strip of carpet. I know that pro installers often (tempted to say always) cut the steps individually and tuck the seams in at the base of the riser. You could do that for just the diagonal steps. You would need a tucking tool which sort of looks...
You can rent a demolition saw with a 10" diamond blade. Around here, they will measure the blade before and after rental and charge you for the wear.
Or you can get a diamond blade and use your circular saw. They are tougher than you might expect. And then you have the blade for future projects.