Yes, you can install, and boot, to an external USB/TB/FW drive, no problem.
No, you can't do that. The ESP that you boot to upgrade the firmware needs to be the INTERNAL disk. Like I wrote, won't work for anything else. This is the main requirement for firmware upgrades via efiflasher and is valid for all Intel Macs.
Up to around 132.0.0.0.0, Apple even required that the internal disk of a MacPro6,1 was an AppleOEM one. At least you can do that now with 3rd party ones - but if you still have an ancient EFI version, you still need an AppleOEM one.
Correct