From your experience, do people typically improv a lot with the script to make it feel more natural?
It can be done very quickly, if necessary. A film can be about 85 minutes, say - so the script is 85 pages, most of that probably dialogue. So your work as a writer is to create the characters via their dialogue and their interactions -- if there are long descriptive passages, the busy script reader will skip them. This is fun stuff, and I've always enjoyed writing screenplays, even when they weren't made into films. Writing a script can take from a few days, to a month or more, depending on the circs.
Some actors say exactly what's in the script. They come to the set word-perfect, or they learn their lines in rehearsal. Others like to improvise around the dialogue, or to change a few words, or to re-order things. When actors do this, in my experience, things usually get better because actors are often keen editors of their own dialogue, and want to communicate their character's intention.