If I turn on the UEFI firmware (disabling BIOS), will my operating systems be damaged in any way or will it be beneficial?
It won't harm them, but it won't benefit them either.
Operating systems that were installed in BIOS mode will just continue to boot in legacy BIOS mode even under a UEFI firmware, and behave as they did before. They won't magically be converted to UEFI boot mode, so you won't get the fast boot benefits you would have had you configured your disk - and the OS - for UEFI boot from the start.
All your hardware being equal, the benefit of true UEFI boot over legacy BIOS mode on a UEFI firmware will simply be a few seconds faster boot time, and maybe a prettier boot screen - that's it. Converting an existing OS from legacy BIOS boot to UEFI boot without a full reinstall is a difficult and potentially dangerous process, as it is likely to require re-partitioning and may even require operating system reinstalls - so it's not really worth doing for the negligible benefit. It'll continue to run quite happily in legacy BIOS mode on your UEFI system.