If you want to remove the existing paint, the simplest way short of blasting is one of the combination stripper/paper products such as Peel Away. Boiled down to basics you apply the stripper and cover it with a coated paper, then after a wait pull the entire sheet off and dispose of it. You do pay for the convenience though, you can go cheaper and messier with lye solutions. One benefit of masonry is you can use caustic strippers instead of solvent based ones.
As a practical matter I wouldn't suggest any variety of chemical stripper if you're going to repaint though. You'd be better served by an angle grinder with a wire cup. A 4.5" grinder should take less than a day while being more useful for other tasks than a 7" one. The grinder is also useful with a grinding or sanding wheel for the occasional rough spot or protrusion.
If the patches are going to be 2" thick or more there's no reason you can't fill in with concrete provided you apply a bonding agent first. You should also dampen the old work in any case to prevent it from leeching moisture from the new work before it cures.
If the patches won't be that substantial then you're better off with a type S mortar if water isn't an issue or a hydraulic cement if it is. The lime in mortar makes it stickier than concrete mixes so it's a bit easier to apply, but it also makes it softer so it's not ideal for large patches.
Cosmetic touch ups are best done with a vinyl patching product, which combines polymers and cement. They're typically sold in plastic jugs alongside masonry mixes. The good news is the polymers allow you to apply them very thinly without cracking, for shallow depressions and small cracks. The bad news is you're typically limited to applying them fractions of an inch at a time.
The exact choice often boils down to experience (and what you're going to mix anyway). From the sound of things mortar may be your best bet, but maybe paste a picture of the large hole to get more informed opinions.