Yes you can run the door straight up the wall and then turn to follow the roof pitch. I'm guessing the door would ride around a foot off the roof pitch.
Yes more expensive. Is it worth it. Depends on the type and if you can relocate your lift.
jstroede you are dead on. I install double track low headroom the same way and the 3800 will have a hard time fully opening the door. Actually the door by itself will have a hard time staying in the fully open position. Traditional openers will keep the door fully open.
You could use a 12"...
I like the arch top personally. In your case the square would look better given you above windows are square. It matches. It's also your decision. You will see more than anybody else will.
I use the shorty DC820B for garage door installations. It does very well working with bolts up to 3/8". I used the heavy corded version for years. No wonder my arms hurt. Anyway, the DC820B will remove the lugs from my service trucks. For me the smaller design works in smaller and tighter...