Need help asking an E46 seller the "tough" questions!

hey friends, very interested in buying this car! it's been my dream to own an E46! $5k is a lot for this car so gonna try to negotiate, but wanted to know what should I be on the lookout for? it seems very clean and well maintained (at least on the surface). they sent me the carfax, but I wish it had more details...

from reading some posts, I saw that I should ask about the coolant system, and the suspension. anything else?

thank you!!!

https://preview.redd.it/et7vww7dyyoa1.jpg?width=720&format=pjpg&auto=webp&s=3a86a85e2f6ab5a472e010ef9234acf25cea3527

https://preview.redd.it/apjueqk4yyoa1.jpg?width=947&format=pjpg&auto=webp&s=0815a6187cd7abea3bee644771c650d361fc8124

https://preview.redd.it/lug4xpk4yyoa1.jpg?width=947&format=pjpg&auto=webp&s=48a56beb172e421634be9a919d683a6f8294cba6

https://preview.redd.it/hprjipk4yyoa1.jpg?width=947&format=pjpg&auto=webp&s=4f9ed8e66899563dc15f878b259932668ccc9d5b