Car:
Yeah, I love the current car, perhaps a bit wider or narrower tracks might be nice but.. as it is it is great.
Tracks:
Personally, I like released tracks.. perhaps a mix of new and the best ones from previous leagues.. but I guess it doesn't really matter as long as we get a reasonable amount of practice time
Fuel:
Certainly. In either way, usual fuel strategy, or a F1 simulation "no refueling", I would definitely want fuel, or it's not F1 for me. If you did a "no refueling thing", all it would mean is set a fuel value which means to get to the end of the race on around 60-100% fuel, and then set the refueling time on pitstops to like 500 seconds.. so you would have to calculate the amount of fuel to get you to the end in practice. But personally, I would prefer the normal way.
Tyre Wear:
Yeah, I believe this is EXACTLY what tyre wear was made for - long races without safety cars/cautions which have a chance for strategy to play out. If you watch the race which I posted up in the SCARTS road racing topic, you can see how tyre's create very interesting strategies.. perhaps, without tyre wear on, the fastest strategy on fuel would be a 2 stop. But with tyre wear, the advantage of the new tyres would make a 3 stop also a viable strategy.. and then, REIROM is stuck behind dede, so he makes a pitstop, gets enough fuel to go to the end, and full tyres (which should go to full very quickly in about 3 seconds, keep fuel as it is).. Dede sees this but decides he likes his rhythm on the low fuel even if his tyres are low and stays out a few more laps until his fuel runs out. REIROM set fast as lion laps on new tyres and is now out in front of dede.. but his tyres have worn 20% in that time, and dede got a shorter pitstop as he had to fill up less fuel.. so dede begins to catch REIROM resulting in epic battle to the finish

That is, if trackmakers all put the same damage line in their terrains, otherwise it would become too hard for league organizers to keep consistency in the tyres. I would suggest quite a low damage number because it easy to make tyres LESS durable, but there is a cap on making tyres MORE durable.
Teams:
Personally, I would want 2 car teams, and both have to wear the same livery. Doesn't have to be based on skill, or anything, but everyone should be in one and they would go for an overall championship. But that's just me.
Qualification:
Yeah, the last system was great, keep it.
The League:
Yes, I like that idea, 12 races.. perhaps the best 9 results count? 3 races is a normal amount to miss over a 9 race period and still be able to contend.
And also, shameless advertising here, can I please direct people to the F1 Race Videos topic - I NEED A COMMENTATOR
EDIT:
Tijny I completely agree with you about the cars.. sure people might crash more often, but I think it would be a great thing if people were discouraged from touching eachother. Atm, you can get away with too much roughness without the guy you are roughing up spinning off the track.. I believe many people would race much cleaner if there was a chance of them pushing someone right off the track and ruining their race or perhaps their own race as they wait for them..