2. I sanded outside on my small balcony and wipe the dust with a rag. Cutting the wood was tricky. I put the cats in the bathroom, wore a mask and did it while running my HEPA filter at full speed. Then I vacuumed any dust on the floor with the Roomba. I cut the wood by placing it on a couple sheets of foam insulation, with the blade depth set so that it would not contact the floor.
After cutting, I moved the HEPA filter around my apartment a bit until the air quality sensor went from red (bad air) to blue (good air), and opened the windows. I know this isn't perfect, but I haven't had any coughing fits thus far.
3. I used an oil based finish (OSMO) that is low VOC, pet, food, and human (children) safe. It's not gloopy or wet once applied, just slightly damp. Cats jumped on it a bunch before it had fully cured without any apparent ill effects, on the cats or the desk.
Definitely an "if will, there's a way" kind of endeavor. The desk is perfect for me though. Just the right size, height, and appearance. Trying to build a stool with the scrap wood leftover, but the wood is quite hard to cut with a jigsaw and pretty heavy.
I think part of what I learned is that it's worth it for me to pay a professional.