William, I can't tell from your initial query if you're aware of this, but the Manesse Codex is early 14thc, not late. There are tons of other illuminations dated to the late 14thc that portray fur integrated with clothing, either as a lining and purfelle or a purfelle (purfelle being the portion that shows on /edges the cuffs, hem, or neckline -- basically, the openings).
That said, there are over-simplified answers and the true, long answers to your questions, which are really rather huge.
Here are some overly simple answers.
1) In the late 14thc, the furs used on wealthy garments were predominantly the sleek, short-haired furs of the Russian (winter coat) squirrel imported to western Europe by the Hanseatic League. There were lots of other furs used, but that one is probably the pinnacle of "typical" for the wealthy. It was called
gris, because it was a blue-grey. Other versions of light fur were pured miniver (white bellies of grey squirrels) and lettice (white/grey weasel). Ermine was generally the highest level and reserved for royal personages, though apparently people used a 'poor man's' version by cutting slits in white fur and inserting black lamb locks through the slits to simulate the look of black-tipped ermine tails. Veale cites that one.
2) I think Elspeth Veale's book goes into some detail about the method, but I don't recall. Also, Charlotte's link above will be useful, and it has the bibliographic reference for the Veale book. That author references primary sources from the skinner's guild in London, so if you really want to get into the detail, those would be the records to chase down. Also, check out
Fur in Dress by Elizabeth Ewing for further historical fur references in clothing.
3) Probably silk and wool predominantly.
-Tasha