

Sorta. OSDMenu does use rom0:OSDSYS but it doesnt matter if OSDMenu is signed or not and as an update path... You can if you want and embed your config file for fastest boot, however it has no hotkeys.
Yes HOSDMenu looks for the needed files on hdd, and you can use OSDMenu mbr for autoboot.
Your confusing things. You can use whatever you want as update path within reason, ie files in B?EXEC-SYSTEM. It can be OSDMenu, FMCB, PS2BBL, ProtoPwn...etc (within reason again)
Read the OSDMenu docs, PCM720 is quite clear on things.
What do you mean you can't enter the browser? MC brower? Again though you are really confusing things...
Try the download out and see.... I have a graph here that explains the boot process as it stands but as stated we plan on changing that for simplicity and to save space: https://ps2homebrewstore.com/umcs/#when-is-ps2bbls-config-called
Substitute signed exploit for whatever you want...and just think through what that signed update allows you do do or not...and how it proceeds