Can I upgrade my laptop CPU

Solution
Probably not. With a very few exceptions, laptops cannot have CPU or GPU upgraded - they are soldered to the circuit board, and the cooling couldn't handle a higher-power part anyway.
Probably not. With a very few exceptions, laptops cannot have CPU or GPU upgraded - they are soldered to the circuit board, and the cooling couldn't handle a higher-power part anyway.
 
Solution
In most cases, probably not. It will likely require you to replace the entire motherboard, unless you happen to have a laptop where the two are not soldered together.
 
Depends on what you want to use it for. Photoshop / video editing points you one way, gaming another, running a terabyte relational database yet a third (ok, that's a contrived case).

And how easily portable do you need it to be?