1. I am familiar with the star players, and am not afraid that they will be transferred
So, will this score stay low, if I am active on the transfer market, regularly selling and buying players?
Essentially yes, but I think it's more about if your selling your best players regularly or not. I think 'best players' are decided by salary as opposed to their role though.
2. The team manager is working hard to improve the team
Is this dependent on transfer market activity, or more connected to the salary of players in your roster? Is there anything else that may have an important impact on this score?
I think your bank balance has an effect on this. If you have a low bank balance your fans don't expect you to be looking to buy players to improve. But if you have loads of money and aren't buying better players the fans don't like it.
These answers as far as I understand anyway, I may be wrong