Concrete – Removing concrete lip at garage

There are lots of concrete cleaning products on the market, but I have had good luck with a 1 gallon solution of 1/4 bleach, 1 cup TSP and 3/4 water. Assuming you are talking about a driveway or garage floor, I would pressure wash the area first to get off the surface crud, then lay on some of the solution and let it set 5 mins or so. Scrub it down with a stiff broom and power wash again. Repeat this as necessary.
As a last resort, you can also use some muriatic acid, but test a small area first to be sure it doesn't effect the color too much.

You're on the right track. I've repaired chips and missing chunks in 80-100 year old public stairways in similar ways. Start with a hammer and chisel, and be really aggressive like a dentist to find and remove all the soft spots.

I've used the tapcon screws, but generally find it easier to chisel an irregular shape that does the same thing.

For your patch I might chisel a channel all the way to the top, so it is easier to get the patching mortar past temporary formwork. Remove your formwork as the stuff starts to get hard, and brush or trowel to match the old surface. Or ignore that as your "concrete restore" will hide minor surface differences.

You can build up the repair in layers, but that requires mixing a fresh batch of rapid set cement every 15 minutes or so.