The CPU is almost certain to be non-removable. If you can't find info about your system or the CPU with a web search, it is not likely you would be able to swap out a CPU in a laptop anyway, which means whoever you bring the system to for the work would be able to tell you what it can run. CPU swapping in laptops is not as easy as in a desktop, even if some CPU fits in the motherboard it still may not work.
The cpu is only avaiable as BGA(soldered connection) and not really upgradable. That model had no other CPU options so even if you found somebody with the proper equipment and training the bios is unlikely to support a different cpu.
The CPU is soldered to the motherboard, updating the BIOS won't help you there. It will cost you more to hire someone to buy and solder a new CPU than to just sell what you have and buy a faster laptop. Replacing major components on motherboards is not very simple.
I go by a very simple rule when it comes to laptops, whatever you buy now you want to make sure you will be happy with till you replace it. Only two things that you can really change in laptops is the hard drive and RAM. Rest you may was well assume you can't change. Some systems have removable CPUs, some have removable video cards. Those are now so few that you may as well not bother with checking and just get the system you want in the first place. 10,15 years ago you had a greater chance of getting a CPU swap to work, not so much now.