Without looking at the wall myself, it sounds like the lime from the mortar that is crumbling has discoloured the black bricks more likely from when there has been rain or bad weather and could also be reacting with the salts in the brickwork.
Blue circle cement won’t be bad, it’ll just be a different colour to the existing whiter lime mixed mortar.
It would be preferable to grind out the joints first to a good depth of 20-25mm then clean the brickwork before pointing back in with an appropriate lime/cement mortar mix .

Sounds like the wall is really old and the faces have blown. If it's too bad to grind and repoint. It will probably want taken down and rebuilding.

Hello clairej_21

If the walls are lime mortar then you should only use lime mortar to replace the damaged mortar. It sounds like you need the wall either fully/partially rebuilt or at the very least repointed, there is no way of restoring a brick only replacing. If the mortar is "super loose" I definitely would not use your pressure washer on it. Pretty sure vinegar would eat away at the mortar too, so maybe best to not use that.

Regards
Gerald

I am afraid you will have to live with the brickwork discolouration which sounds like effluressence which will gradually fade away over time after repointing.
As far as repointing is concerned i would give it a good raking out and repoint using lime mortar, ( no cement). Good luck with that. Regards, mick.