Solved

Intial Car Design

From my understanding, your initial car design at the start of the season would be at it's optimum if you competed in all 17 races from the previous season.  Is this still true, or is there now a minimum number of races you have to participate in the prior season to get the strongest design?

Joshua

Yes, if you compete for an entire season you will receive maximum possible design. But it is way more complex than that because the star rating of your CD(s) influences the initial design and you can get a better design with multiple CDs. Six races is all you need from a five star CD to hit the design cap in Elite.

I reckon 15 races with a 5 star CD would result in a better initial design than 17 races with a 2 star CD. If you have had a bad CD for most of the season and manage to find a good one in the last couple of races you can also optimise the starting design by leaving and re-joining the league which appears to be a trick employed by quite a number of managers. 

Also have a read of this... Next season's car

Alright.  Do you think 8 races with 4.5 star CD and TD would generate a car that's competitive at the start of the season?

It would depend on promotion/relegation how the other teams have managed the cd positition for the season level and build of hq for starters and what you mean by competitive in comparison with a another team that used a 4.5 for 8 races possible but that would depend on sponsors so as you can see it not a yes or no answer

Compared to teams that spent entire previous season with 4.5 or higher CD and TD. And by competitive, I mean almost annihilating the competition.

If your competition also used 4.5 star CD for the entire previous season, you should be roughly equal on car development.

Yes

But should a team that did only 8 races with 4.5s be dominate?

Initial car designs would be more fun if there was changes.
1 Designer you have one thing 100% built everything else 1 point and then add in suppliers
2 Designers you have 2 things 50% built everything else 1 point and then add in suppliers
3 Designers you have 3 things 25% built everything else 1 point and then add in suppliers
It allows teams with big money to have a show of strength but at the same time doesn't allow them to dominate as lower cash teams can use research to catch up where as the big money team can't. 

Don't make sense. LOL
Team with 3 designers can only work on 1-2 areas each race.
Team with 2 designers can only work on 2-3 areas each race.
Team with 1 designer can work on 3-4 areas each race.
All boils down to what way people build their cars each season.

Starting at 1 point, everything in the car design matters. Where as with the current levels of design. Cooling, reliability, fuel and tyre economy levels don't have much of a say.