I think I need to replace my fan clutch due to temp problem, but before I do anything I would like to ask your advise.

My car had overheating problem a week ago.Temp went up very close to 120C and boiled over(coolant spilled out of the expansion tank).

I have since replaced the thermostat(I used 89C T/stat), and had the radiator serviced (rodded out).

Today at about 75F outside temp as shown on my dash, here are the temp readings I observed:
*Freeway driving:85C to 90C
*City driving with minimal traffic:90C to 95C
*City driving with stop and go traffic:95C to 100C

Are the above temp readings normal for the outside temp of 75F?

Do I need to worry about my Fan clutch not working properly? Should I replace the clutch? Is there a simple way to test whether or not the clutch is working properly?

Can you suggest some tips for a DIY in replacing the clutch?

How much do I expect ot pay for a fan clutch?

TIA