* Will a 2 inch electricians bolster + rubber mallet be OK for removing
the tiles (traditional brick + plaster wall).

Provided you replace the rubber mallet with a big solid hammer, it will
work, but will be a considerable effort and will leave large lumps of
adhesive and shards of tile. Using an SDS chisel will result in a pleasant
job that removes the tiles whole, with minimum adhesive left behind.

* Once the tiles are removed, what can I use to flatten out any
remaining adhesive -- chisel, screwdriver etc.?

I remove any large bits with the SDS chisel and then smooth off with a belt
sander and coarse belt.

* I was thinking once the tiles are off, maybe it would be a good time
to paint my skirting board. I can then retile and get a neat finish
with no paint drips on the tiles. A good strategy?

Does gravity go upwards round your way? ;-)

I got the best results by remove the skirting, tiling and then putting new
skirting and coving on top of the tiles, using caulk to fill between.
However, this is far more effort than what you propose. Personally, I think
you are more likely to get adhesive and grout onto the skirting, rather than
paint onto the tiles, which will clean up without problem anyway. Therefore,
I would paint last if keeping the skirting, using an acrylic paint.

Christian.