IF the laptop works, I would leave it alone. If the system won't power on, then you'll have to remove the board anyway, unless you want to replace the power supply first, to see if that's the problem. I tried replacing a laptop board once, and never again; the connectors are tiny and proper grounding is a problem when reinstalling the board. These boards aren't upgradable for the cpu; even if you were able to use a faster cpu, you'd have to find a better heatsink with the proper connection to the board.
Yes but I would check to see what CPU is the highest the model supports.
That said, having worked on a number of laptops, getting to the CPU is a pain the you know what for most of them. Very few give easy access to the CPU. You will want to take some tape (masking tape) and label the screws if you want to go for it.
But I suggest not doing it. Most laptop CPUs cost about $500 +. Very expensive.