How to match this brick

Q1:

I would try a stiff brush and water. If this does not work, you may be able to try a muriatic acid solution, but I would look at the manufacturer's recommendations first. Depending on the brick color and type, this may discolor the brick.

Q2:

• Apply the grout using a grout bag to minimize the mess.
• When the joints are filled, wait until the grout is the consistency of wet beach sand.
• Go over the joints with a brick jointer.
• As you are jointing, periodically wipe down the brick surface with a wet mason's sponge to remove any grout from the brick face (clean the sponge out in a bucket of water as you go).

Three inch gaps seem quite large - even for a 300 year old wall.

You just need to use a good mortar mix (sand and cement) on the narrower gaps.

Clean out all the old, lose material first to make sure that you get good adhesion and then push the mortar right into the gaps as far as it will go. Work on a small area (1 m²) at a time.

Adding pea gravel to give the mix more "body" might work on the wider ones.

However, I'd get a professional to have a look at the wall first to make sure you're not going to have to redo this work in a couple of years time. If the foundations have gone it might need something more substantial work doing.

Is the wall part of a house or just a garden wall? If it's the latter then dismantling and rebuilding might be the best long term option.