These are great questions!
I'm going to break down my response into two sections:
- Building the machine
Don't breathe flux, if you can do your soldering outside. If you can't, put an extraction fan by your workstation, so the fumes don't get inhaled. If you want to be extra safe, wear a face mask, and gloves will soldering and working with the chemicals. When you're done working on the board wash your hands thoroughly
- Using the machine
If you know the entire build process is lead-free, I don't see any issues of touching the board during daily use. If you're not sure if it's entirely lead-free, you can put a chloroformal coating on top of the board, usually used for waterproofing, but that'll prevent you from having direct contact with any of the heavy metals. You can use hot glue as well. Chloroformal codeine can be dissolved later if you need to redo a joint
- Advice on solder
Unless you're a large manufacturing laboratory, it kind of sucks to work with lead-free solder, you have to use higher heats, it requires more technical skill. Especially if you're new to soldering, I would recommend using leaded solder anyway. Just don't breathe it, don't touch your face, wash your hands after. The lower temperature will give you a higher chance of success.
In either circumstance, get a practice old circuit board, desolder and solder things until you're comfortable with your heat management. You want to use the least amount of heat will still getting the job done