Howdy!
1. Certain design attributes are vital at various courses. It's up to you how you design your car and what to research for improvement. Though there is currently a bit of a bias on a couple attributes that combined dominate over the other ones, I believe it's important for all new players to figure this out on their own. The reason I say this is because I'm positive in the future these biases will be balanced out. I'm sure somebody else will come along and give away the answers (to which they already exist on this forum in other threads!)...but what's the fun in that! Have you discovered yet when hovering over the icons of design attributes, a small box appears to briefly explain what each attribute does?
These helpful boxes are available across various areas of the game.
2. When your car isn't being repaired, it's not going to churn out laps like it does when its fitted with fresh parts. If the parts on your car begin to fail, which takes a few races of non-repairs to happen, the car is likely to retire during a race.
As for manufacturing, you should click here to learn how important the manufacturing facility is.
3. The Chief Designer helps develop next season's car with emphasis on their strength and very little emphasis on their weakness. The Technical Director...well, I'm not really sure what a Technical Director does currently.
However, the Chief Designer and Technical Director combined, influence the amount of progress you are able to make when you research other teams whose design attributes are better than yours. This is all based on the number of stars your CD & TD have. For example, a 5 star CD and 5 star TD will give you 5 stars in research, which means you will reap all the possible research design progress. If your CD is a 5 star and TD a 4, or 4.5 star, your research power will be 4.5 stars. It's quite like an average of the two star ratings together.
4. I don't really have a clear enough answer for this.
5. Every facility is essential to success each in their own way. Many players develop the core facilities first, like Design, Manufacturing, Technology, and the Simulator.
6. Sponsors don't currently have "goals". Before the start of every race, right after qualifying, you can view your race objectives on the home page (try refreshing if you don't see it). Who you sign with doesn't matter, but sign with a sponsor that fits your needs.
7. Many players spend tokens in various ways. If I were to guess, the most common way tokens are being spent right now is in exchange for in-game cash to continue funding their teams, as some players reported being in the red all the time. Some players spend tokens on healing and then training, then repeat that process, others spend it on engines, some spend it on changing Drivers & Staff names/nationalities, etc.
8. It's true, real strategies don't seem to work. There's some serious math (unlike other F1 team management games) that goes down to simulate the game and it calls for different strategies.
If you'd like to learn some strategies, you can always review previous races from the current season to see what the winners are doing.
In conclusion, you've only completed 7 races in iGP so far.
When I completed my first 7 races in iGP, I would always run Super Soft and roast them into the ground...
Give it some time...you will gain a surge of knowledge in your second and third seasons as you see yourself begin to improve.