The research on my car is showing red for most of my aspects, and I'm barely gaining any research on any part of the car. Any idea what I'm doing wrong?
Research is calculated on the difference between your design and that of the strongest team in the particular attribute you are researching.
A red tick indicates you are the strongest team and researching this attribute will yield no design points.
There are only three teams in the league, you and two others. Do you know if the other two teams are active? If they're not, they won't be assigning any of their Design HQ generated points so you will always have the strongest design.
To get the best experience you should consider looking for a league with a more active Pro tier.
Currently there's only one other active member, and he seems to have caught up fairly quickly so I think the research makes sense. As far as me having the best design, that might not be possible because even so, the other player is still way faster than me. Its almost impossible for me to catch him anywhere, when I'm pushing with battery and he's casually getting away