Ok, I'm going to try to answer your questions.
The fan and Heat Sinks do change from a certain processor to another, the material, the form factor and the fan speed change depending on the needs of the processor and the Thermal Design. On your processors, the difference in core speed makes them use different and more specialized Heat Sink that is able to cool down a the processor. The biggest difference came for processors with a core speed higher than 2.8GHz.
If you wish to utilize a 3.06GHz processor on your motherboard you will need to make sure that your processor meets the requirements on the supported processors list for this motherboard, use the stock Heat Sink that came with your new processor (if boxed). If your processor is not a boxed unit and did not provide the Heat Sink you will need to try to get one from your closest retailer.
The Intel(R) Heat Sinks meet the standards required by the socket manufacturer and or motherboard manufacturers. In your case your motherboard is Intel so the Heat Sink should fit correctly and should be secured.
Here you can find the supported processors for your motherboard:
Also it will be a good idea to have the latest BIOS installed on your motherboard, you can find the BIOS update here: