Seems early for cavity wall. I would guess the problem is the high concret level out side. It my 1870s house the was a bitumen damp course which had been built over . By taking down below this level it helped a lot.
Later interventions affecting the performance of historic buildings are...
I would spend less on downstairs and turn bathroom into kitchen. Have a loft conversion instead so you gain an upstairs bathroom and keep it three bed.
Though using a waterproofer on old bricks will trap any moisture in them causing damp they should be permeable and able to breathe https://www.spab.org.uk/downloads/Courses%202011/LDN%20HOW%20-%20Breathablility%20and%20Damp-%20Davids%20Version.pdf
Apparently you need to cover the foam with some kind of membrane to avoid damp. I'm guessing but not clear from your question whether you intend to do every internal wall rather than those that face outside? Also try and make sure that you salvage any skirting rails picture rails etc if you...
There's no need to remove woodwork with lead paint it is only an issue if stripping. Pine would never have been exposed in victorian times. It is much better to keep original fabric where you can rather than creating a pastiche.
Why do you need new skirting. If the existing is victorian you should keep that. It will be seasoned wood rather than mdf. If not ask your neighbours to see what they have as this is often the best guide if houses were built at same time. The link doesn't look very victorian whith the bit...
Victorian pine doors were never ever exposed pine this is a 70/80s thing that lingers. Don't worry about matching from an authenthicity perspective. You could just paint all white and they would match.
Male sure you read SPAB's damp advice.
https://www.spab.org.uk/advice/technical-qas/technical-qa-20-rising-damp/
If you put a membrane underneath it will push the water elsewhere I would have thought. Stope the water getting in. If the water if coming through the tiles it will eventually dry...