minimum and maximum fan speed would depend on a few things--which cpu you have--is it overclocked--how big is the fan--is the fan bios controlled or otherwise controlled --how good the case cooling is
the bigger the fan the slower it can spin
if you replace the heatsink then yes you should use thermal paste--its not always white and you need to apply the right amount--too much is bad and too little also--look on youtube to see how to apply it--you can buy far better thermal paste than what usually comes on a pre-built pc quite cheaply