I can only speak from my brief experience in fixing EL-Nikkors, Rodenstock something and some cheap 3 element type.
First and foremost.... if it takes more than light "umph" to unscrew, stop! It's not supposed to take "grrrr" kind of force. When you take an element out, be sure to note, which way it is supposed to go back in and what order. I usually take quick photograph to remind myself. I mark lens element with a painter's masking tape to indicate which way is up.
EL-Nikkors unscrew from front and back. All I do is to take a largish rubber balloon, put it on my palm, press hard against it, then twist. I also have a set of small screw drivers. I really haven't needed them. To clean, I use the ordinary lens cleaner and some microfiber cloth. Once clean, I use clean cotton gloves to handle them. A can of compressed air comes in handy as well. As to a work table, I use a very large micro-fiber cloth. Nothing rolls off and nothing gets scratched.
I was actually surprised fairly bad dust and fungus came off cleanly. Then again, I had a Rodenstock that multi-coating was damaged so badly, as I tried to clean, chunks came off. I then used tooth paste to take it all off, re-assembled it, and I gave it away for shipping. (noting what I have done)