MacBook Pro fan not working properly

SMC which controls the fan gets thermal data from the sensors within your system. Depending on what they are reporting to SMC the fan will engage and as it’s a variable speed fan it will run at different RPM so the air flow across the cooling fins will be at the needed intensity to shed the buildup of heat. Apples thermal template algorithm is designed to be less aggressive at the lower thermal load so it does take a bit of load for the fan to start up.

From what you are stating it sounds like your system is running as designed.

The ability of your monitoring app may bias your view point. As you can’t see your fan physically and a single snapshot may not offer enough granularity on what’s happening, You should try an app which records over a period of time. I personally prefer this app TG Pro as the full version will get you that.

You do appear to have dirt on your screen or is that damage?