One of the biggest rules of installing gas piping or appliance connectors is that whenever you screw metal to metal to a line that will be delivering gas with no thread lubricant, 10 times out of 10 it WILL leak. It's just a matter of time.
No, you need to replace the fittings and the hose every time you hook up a new appliance. That’s why they sell them in a kit; they are not designed to be used more than once and it’s really not worth risking it.
I’m not an expert, but in my opinion yes you can put pipe dope on the gas valve male connector. Just don’t put it on the connectors for any flange style fittings like I show the video. The “pipe dope” sealant is stronger than tape and designed for permanent connections under pressure. As far as I know plumbers use the pipe dope sealant for gas connections and some even use both. Personally I would not use the tape for gas connections.
Most plumbers seem to use pipe dope, no tape. I once had the gas company for my city come out and do a repair. They used pipe dope not tape. Use that information as you want because I’m not an expert. Both are probably fine, but it seems that the “professionals” don’t use the tape.
If you have a plastic threaded connection and you use pipe dope you have to read the instructions on the tube/can of the pipe dope to ensure it can be used on plastic. NOT ALL PIPE DOPE IS APPROVED TO BE USED ON PLASTIC. If you use pipe thread tape for gas you must use the yellow teflon type tape. The white teflon tape is not approved to be used on gas lines. I am a retired inspector and have rejected hundreds of inspections for these two simple things.