Walls – Should a concrete curb at a patio door be built on top of or inset into the slab

It might work - however the problem would be where the centre uprights join the horizontal sections.

This piece of ascii art might help:

||========||
||   ||   ||
||   ||   ||
||   ||   ||
||========||
||   ||   ||
||   ||   ||
||   ||   ||
||========||

Where "||" is the vertical sections and "==" the horizontal.

You'll end up with two sections like this:

||====    ====||
||   |    |   ||
||   |    |   ||
||   |    |   ||
||====    ====||
||   |    |   ||
||   |    |   ||
||   |    |   ||
||====    ====||

As you can see buy cutting up the centre you are cutting through the middle of the joints which will weaken the joints and they could come apart.

These joints are mortice and tenon and you could try strengthening them by putting a dowel through the tenon before cutting:

Drill all the way through, insert the dowel (with glue), plane and sand smooth. If you're painting the doors you won't see the join. To drill the hole straight you could use a portable drill guide or a plunge router.

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.