Should you repair the entire floor before refinishing a basement or go room by room
I'd definitely want to do all the grinding first. You'll probably have to rent the grinder and why do it twice. Also, you'll get grinding dust everywhere unless you really wet it down.... messy. When you frame the rooms, you don't want protrusions.
The filling in could be done as you go along because the rooms are divided. Being level isn't as important as being flat. I've been in many residential construction sites and have seen very few totally level foundations.