So... why didn't the demon just go to the monastery on his own? Why did he need to bring other people along for the ride?
Probable due to some sort of rules. The general reason in stories like this is demons are bound by rules set by God that limit them. In this case the demon had to be carried to the monastery. It just couldn't go there itself.
It's also possible it just didn't know where the book was and needed people who did know to take it there.
Why did they waited till there was only one book left to copy it? They could have did this before there was only five or ten of the book left.
The demon destroyed all of the other copies. The monks probably wised up to what was happening a little too late. Either that, or the demon works very fast and effectively; maybe they did copy it before, but the demon destroyed all of the copies until there was only one book left.
Don't forget, they didn't have photocopiers or even printing presses. They had to make their copies by hand. You can destroy a book a lot faster than you can make a new copy by hand.
Presumably the demon started off not knowing where the last copy of the Key of Solomon was. Once the demon learns this and is put on the road to the abbey in question, there really is no need for the human escorts. Not only can the "witch" ultimately fly, she's clearly physically stronger and more durable than any of the mortals and has no apparent problem entering and operating on holy ground.
Maybe the demon could only enter holy ground if brought in by humans.
Or maybe his lesser demon lackeys needed time to spread the plague to that remote monastery.
How the hell could Ron Perlman's character be buried during the final scene in the movie when he was incinerated?
Ashes or whatever was left or just an empty coffin used as a symbolic burial.
The demon wants to get rid of the last copy of the Book of Solomon, which is the only protection that humans apparently have against the Forces of Darkness. The book is stored in a hard to get to monastery that almost nobody ever goes to, instead of, say, Rome. When they get there, the monks are all dead. In order to assure that the book is lost or forgotten, the demon wouldn't have to do anything at all. Instead at the end, the book is now in safe hands, presumably on its way to another scriptorium so they can make more copies. Nice Job Fixing It, Villain
To quote Debelzaq "If the book were in the demon's hands, we would face an endless darkness". The demon wanted to hold relatively large amounts of power over humanity (to destroy it entirely) through the book, thus it needed a copy still around.
To clarify the above poster's quote of Debelzaq, keep in mind that spell books rarely contain a single spell, just like a hymnal rarely contains a single hymn and like a book rarely contains a single chapter. The spell book with a containment spell would also likely have a few summoning spells, a few controlling spells, some plague spells, and maybe a doomsday spell or ten. As well, the good spells could be studied and counters created. And as a final nail, the rare spells (like the containment spell which only exists in that book) would be under the demon's constant watch so any opposition wouldn't be able to readily defeat her.
On top of that, the monks are believed to be copying the spell book and are not known to be dead. Hence why she is being delivered to them instead of to a monastery where the monks are actually alive. So at the very least, it's not unreasonable for her to want to go there, kill the monks protecting and copying the book, and either steal it or destroy it so that no one could use it against her.