I use Anti-Ban EBOOTs on all COD games when playing online, even though I don't mod anymore on them unless is a private match with friends, its better to be a bit safer than sorry.
It would depend on what else has been done to the EBOOT to where its was safeish. Generally speaking using anytype of mod carries a risk of a ban from PSN. All an Anti-Ban EBOOT really does is attempt to block some of the automated params on the games server side... it has worked for me for years, but toher have not been so lucky and goten baaned for next to nothing, so its pot luck and at you own risk playing online in CFW and always has been.
No its not needed. I have never done this in all the years I have used CFW. I mean if you really wanted to do this then you could, it will be loaded back into memory on reboot anyways but I don't see the point in it really.
IF using a Cobra CFW it will block the ability to use homebrew after the syscals are disabled anyways so you cannot use it until you reboot and if using a Standard Non cobra CFW then PSN Patch will also block homebrew from being used once the syscals have been disabled.