the main use for chaintugs by most people is for easy setting (micro adjustment) of chain tension when a wheel needs to be removed and then replaced. You don’t and shouldn’t need a chaintug to hold the axle in place. The axle nuts should do that. If they don’t, then they need to be replaced. If you want to use chaintugs, realistically you only need one. Most people would place it on the drive side (side with the chainring)

setting chain tension and getting the wheel centred can be a fiddly thing, especially if you don’t have any experience. But it’s completely possible to do without any chaintugs. My advice would actually be to practice at home, at setting tension and centering the wheel. You should be able to develop your own way of doing it easily enough. If you need help, there are plenty of video tutorials on YouTube, and I think a video demonstration would be more helpful than me trying to spell it out in a block of text. Someone else might be able to chime in with an easy to read checklist of procedure though.

yes, the tension is set by “feel”. But the general rule is that it should have no more (or less, realistically) than half an inch of slack (up/down) movement. A little slack is much better than having it too tight.

Fixing a flat with the wheel still attached? Nonsense. Practice removing, replacing, setting tension and centering the wheel. Once you’re well versed, pulling the wheel off to fix a flat should be a quick, simple procedure.