Hello,
Red checkboxes within the research tab indicate that your car is the highest in that attribute -
researching these attributes is pointless, you will gain 0 design. Spending your DP in these areas will have the same effect as usual.
To answer your second question, changing your staff won't cause any changes to the checkbox colour. The only way the checkbox colour will change is if somebody else spends their DP to a higher point than you have.
There is a tutorial on the forum which helps to explain in a little more detail how car design works in iGP Manager - I'll link it
here. Section 3 focuses on research.
I hope this helps, but if you have any further questions, feel free to ask.