May be best to see details, use ppa version with your live installer (2nd option) or any working install, not older Boot-Repair ISO:
Please copy & paste link to the Boot-info summary report ( do not post report), the auto fix sometimes can create more issues.
You can check if install is UEFI or BIOS. But how you boot install media UEFI or BIOS is then how it installs. The UEFI settings in UEFI/BIOS are only for the system once installed. Often best to have UEFI Secure Boot off, but then you have options to boot in either UEFI or CSM. CSM - UEFI Compatibility Support Module (CSM), which emulates a BIOS mode, only available with secure boot off.
But how you boot install media is separate. If Secure Boot is off, you should get two boot options for the live installer. One clearly UEFI and other just description of flash drive. My system has UEFI:PMAP or PMAP to boot live installer. The PMAP only is BIOS boot. Most use name or label of flash drive where mine had PMAP.
[ -d /sys/firmware/efi ] && echo "EFI boot on HDD" || echo "Legacy boot on HDD"
If using legacy/BIOS/CSM boot on a gpt drive, you need a bios_grub partition. For UEFI boot you need an ESP - efi system partition. Best not to use MBR(msdos) with UEFI. Windows does not allow MBR with UEFI, but Ubuntu will let you install that way. I suggest always using gpt now. The only time to use MBR, is if drive will have Windows booting in BIOS boot mode.
In UEFI you often have to turn on allow USB boot or full USB support or similar setting. If Secure Boot is on, USB boot not allowed as not considered secure, so allowing USB boot is a separate setting.