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In this way, can I change my CPU cooler?
You can re-use the CPU cooler from your current system or replace it with a new one, but if your new CPU doesn't include thermal paste in the package, you'll need to get that as well. Thermal paste helps conduct heat from your CPU into the CPU cooler, and it's a necessity.
Similarly, can you put any fan on a CPU cooler? Fans for CPU coolers are generally designed for a higher static pressure than case fans. And yes, CPU cooler fans are generally speed controlled so that it will run slower and quieter when there is little load on the CPU and ramp up when load and heat increase.
Keeping this in view, should stock CPU cooler replace?
1: Compared to aftermarket coolers, stock CPU coolers feature a very poor thermal performance that can lead to your PC components being damaged. 2: Stock CPU coolers produce much more noise, which can be distracting and bothersome. 3: If you are looking to overclock, an aftermarket CPU Cooler is essential.
Do you really need a CPU cooler?
Yes you need a CPU cooler. If you're buying a retail CPU package you'll get the stock CPU cooler included in the package. Thats fine if you don't plan to do any overclocking of the CPU.