That's the process, but don't expect it all to happen quickly unless you've really planned it out.
It took us a while to get my name on a bill for proof of address to give notice.
Once we had that, all the appointments to give notice were booked a month out so we had to wait....
After we had our appointment to give notice booked, we scheduled our ceremony (register office) and those were booked a further month out (a month after we gave notice). Luckily we had a small wedding so we didn't need to coordinate the date with anyone besides our two witnesses.
After we knew the date of our ceremony, we booked our in-person appointment 6 weeks ahead of time.
In the end, I arrived 27 July 2012, we gave notice 10 October, got married 10 November and my FLR was approved 10 December. The whole process took a lot longer than I thought. Still well within 6 months, but longer than I thought....
Of course, if you're getting married in a church or already have it planned out a bit, it won't take that long, but don't underestimate how much planning it takes when you're on a timeline (6 months for the Fiance Visa), you've got a partner who's relocating and needs proof of address in the UK to give notice and you've got to book the in-person appointment ahead of time. It'd definitely do-able, but just be sure you're realistic about how quickly it will be done.
To answer your second question- no, she won't need to leave and reenter with her FLR once it's approved.