Looks you installed /e/ using the easy installer, yes?
Please don’t try to lock the bootloader yet; it looks like you may be at risk of bricking it if you do.
If you updated FP4 to the latest android 12 before installing /e/ it would have been on Security patch for March 23.
Your safest course of action is to wait for /e/ to release the next update for FP4 which should contain the March 23 security patch. While you wait you can learn about some of the things you need to know in order to make a plan for locking the bootloader.
Locking and unlocking the bootloader triggers a wipe of the data on device so you will lose all photos, files, apps you may have installed etc etc. So that’s an added inconvenience for you!
Questions 1. and 2. can be answered using the installation instructions as a starting point.
Q 3. The current state of OEM unlocking toggle in Developer options I would expect to be greyed out with info saying bootloader is already unlocked, yes? It should be optional to toggle it back on after locking the bootloader.
Q 4. No, because we don’t know what OS version you updated to. Best guess would be March.
Exactly what version of eOS is on device at the moment?