You dont HAVE to spray the stain, but it can save quite a bit of time, especially if you are using a prestain, and on big doors. You have to spray it on kinda heavy, especially if your using a lacquer stain. Heavy enough to make a bit of a puddle. If you fog it on, it dries in before you get a chance to wipe it. I do as much outside as possible. I always spray on the sawhorse, then grab the boards by the end, and lean them right up against the house to dry.
As far as jambs and windows, I dont mess around with spraying the stain or prestain. I only spray that stuff outside.
Before submitting a bid, remember that the base and case need to be puttied at some point. Usually, builders will let you slide by prefinishing the base and puttying after installation, but on jambs and windows and stuff, its best to putty before the final coat. I did work for a company that made a deal with the GC so we prefinished all case and puttied afterwards. Personally, if I have to spray lacquer over the putty, I only stain the boards beforehand. I dont lacquer them down. I dont think its worth it myself.
Also, ask about caulking. We always had to caulk the wall to the trim, and it takes a lot of extra time, cuz it needs to be wiped REALLY good. If you dont realize thats part of your job, you'll be eating a lot of time. A lot of places dont want them caulked though.