I'm gonna do my best to answer a few of your questions and give some advice here. Almost all of your questions relate to iRacing generally, and not specific rules or operations of the ChampCar iRacing Series. Dan Sosulski has a video series he's doing right now which is an introduction to iRacing and it may give you some tips to improve.
When you're in the car, the 'Tab' key cycles through the different timing options. Often you'll have the 'delta bar' enabled in Practice and Qualifying, but not in the race. You can enable it in the race if you want. I find the 2 most useful deltas are 'session best lap' and 'last lap'. Other options like 'all time best' might frustrate you as you try to keep up with a pace that's not possible in the current weather and track state.
You'll know that F1, F2, F3 keys etc give you different 'black boxes' with information, of course the F3 black box with the relative information is usually most useful in a race, you can briefly look at the F1 box and it will tell you how much time remains in a session. During a race, it will tell you how much time is left on the race clock.
Sounds like you know to have 'Fast Repair' checked in the F4 box of the pit options. I've looked at the replay and I'm not sure what happened with your repairs. What I did see that you used the tow truck after your spin. Even if you have a fast repair, towing the car back to pitlane in a race session will almost always be slower than driving back to pits unless you've blown the engine. The other thing to consider of course, driving a damaged car around the circuit may be difficult to control and keep safely out of the way of other racers.
If you've raised your iRacing Safety Rating high enough to be eligible for the championship rounds, you're already aware of incident points and that you want to avoid them. You'll also know that a qualifying lap with an incident isn't counted. Almost all of the time, bump drafting gives both drivers a 'contact (0x)' or worse, which would invalidate their qualifying laps.
Some drivers might choose to leave the pitlane together in hopes of picking up a draft though. Down the back stretch at Road Atlanta this is probably more noticeable and effective than Sonoma and VIR South, the next 2 races on the calendar.
Trying to 'pick up a tow' in qualifying only really matters once you've already registered a lap time equal to the best you can do unassisted. If you're unsure, I'd say your best option in qualifying is trying to find some empty track you so can focus on your best, smoothest, cleanest lap, without having to worrying too much about other drivers around.
In iRacing, different cars have different pitstop fueling settings, these replicate the kind of crew and refuelling rigs which would be used with that kind of racecar. How specific you can be with your fuel request is covered by this, and as such for the NC Mazda MX-5 it's only possible to select in increments of 1 gallon.
Can you imagine a ChampCar driver radioing the team and asking for 5 and 3/4 gallons?
So in conclusion, I hope my little thoughts here make sense and help you be more comfortable and competitive next round. You were scored as completing the race, so you're one round closer to your name going in the hat to win a very valuable free ChampCar entry.
Hope to see you for the race at Sonoma on Feb 12! (Check back soon here on the forum for details of the practice sessions in the weeks ahead)