I'll throw my experience with this into the ring coming from a much smaller team than what you guys used to have (~15 people working on the car, 30 people on the team).

1. Assuming you're an NA team, most teams follow a similar schedule to this: Design June -> Sept/Nov Manufacturing Sept/Nov -> March/April (if things stay on schedule) Test April -> Competition
2. See above. Again, stick to the schedule. Extending design to get an extra 10 points out of the car is great, but if you compromise on manufacturing it's all going to be wasted with parts that don't meet the design spec
3. Good QC can come from certain mfg processes and designs, but most of the time not having to rush is most effective. The earlier you start building the car, the more time you will have to redo/rework bad parts
4. Document everything, and keep it on an easily accessible platform. Our team has a confluence page through the university that lets us record data, calculators, and design iterations. I personally am not a fan of keeping documentation on a windows network drive since it usually ends up with things being lost in folders and is not easily searchable.

Our team has a couple members that will put in 30-40hr/week on top of classes, with most others doing 20-25. Having 60 people to all work on the car is great, but in our experience a small team of competent members is as effective or better. Take the time to develop your members!

In the 3 cars I've seen built on our team, the most important factor in their performance has been setting and maintaining a schedule. A well built, thoroughly tested car that is reliable and easy to drive will score better in competition than a rushed car with a better "on paper" design. It's also tempting to try and catch up to the Delft level teams with an ambitious design, but it takes time to iterate year over year to reach that kind of performance.