Most of us went through a trouble spot relearning BLM at 60 but it gets significantly easier with time. You start seeing patterns and workarounds, and just accept the failures as something that's bullshit or something you have to work around. You don't even really have to keep an eye on the Enochian timer remaining unless something "changes" like procs or movement or low MP due to something.
For your questions:
Typically keeping up Enochian has priority over your current rotation. If you have to sacrifice one F4 (which happens semi-commonly with procs) to keep up Enochian, yes you sacrifice the F4. It has to be a case-by-case reason to not uphold it, such as a strict DPS check or having a very soon Sharpcast/Enochian anyway.
Renew Enochian before the start of a new rotation, or around the start of a new one ... usually. The timers line up so that you get three rotations per Enochian usage. You always use Sharpcast with Enochian.
Yes your examples of rotations are correct, assuming the MP ticks work out properly. Very rarely can you do B3 > T1 > F3, just saying.