Of course it can. What did you expect?

https://doomwiki.org/wiki/Doom_UEFI

Depends on the version. All of them (the newer ones with networking) have TFTP. Some even have HTTPS. I think HP Servers even have HTTPS-Boot with client TLS certificates.
None of it works with Wifi though. iPXE has wifi support for some devices but you obviously can’t start it over the Internet. You need to flash a ROM you don’t need or use a USB drive to load it. Then you can boot Linux from the Internet. (That also works if you don’t have a UEFI Shell in BIOS). https://netboot.xyz can also boot other OSes than Arch.