Can I change my MacBook Pro battery my self ?

Many more recent MacBook Pro models have the battery glued in place. Replacing it is complicated, messy and may require hazardous chemicals. So much so that Apple does not replace the battery in stores, or even in depots. Instead, they replace the battery-keyboard-trackpad-top-plate as an assembly in stores and depots.

The after market batteries you can buy on bay are awful. OWC MacSales has some that are passable.

You are better off with an Apple battery, and they will generally replace it, complete with regular 90 day repair warranty for about US$250.

I strongly agree with ku4hx. Unless you have experience with repairing electronics, this is not something you want to take on. Sure, it may seem like it's cheaper until something goes badly wrong and you're left with a computer Apple might not service because you opened it up.

Generally NO.

What model-year MacBook Pro, what screen size?

No ... well yes probably maybe. But unless you are experienced at MacBook repairs/replacements it's a bad idea.