"The previous owner applied some terracotta render of some kind that looks like it's been keeping the water in or something, but I'm not sure."
that does tend to damage bricks, but its more often applied after brick damage as a cheap patchup.
"What else causes spalling?"
Water ingress, freezing, render, and inappropriate cleaning methods that strip the brick face off.
"Is the fact that it seems to be mostly at the bottom by the windows significant? I wonder if I need to mend my
guttering or something?"
Probably gutter or the window channeling water there. Lot more common at ground level.
I'd check your drip grooves on the underside of the window sill, mak sure waters not running onto the wall. If theres no groove that might be why.
"As to mending them - do I have to do an Arnie and hack out the spalled
bricks and replace them? I assume that's the only way."
the only decent way, yes. Not difficult if youve got soft bricks, but do take real care not to break other bricks in the process. soft bricks are remarkably weak.
Always take a piece of brick with you to get an exact match, failure to do that is a recipe for a cockup. Patching with bricks that you thought matched but turn out not to will look real bad.
You could also cement the face of the damaged bricks as a patchup, but a) it looks crap b) keep the cement off neighbouring bricks. Lime would be much better for that, and it doesnt matter if it gets onto the sides of the other bricks.
"I'd like to get rid of this render while I'm at it, but will that damage the brickwork?"
Probably. Best move is to ascertain if your bricks are soft or not. If they are, proceeed only with the greatest of care, or youll end up trashing half of them. If you cut the remaining half of a damaged brick with a stanley knife, theyre softies.
Another approach is just to leave the render to fall off in its own time. Very slow though, and its going to look a mess for quite some time.
Dont paint the bricks.
NT