Yes - I use a Dremel cutoff disc and a magnifying lamp. I then test on a scrap to see two spirals before using it on anything valuable.
Yes - a #57 drill simply causes tap breakage. Never use a drill smaller than recommended, no matter the size. Henry Pearce told me he always used one size larger, and his kits are still bulletproof.
Some cutting fluids are better than others - the little yellow can from Ace is ok. Never tap dry, and never use just plain oil.