"Mixing different types of RAM"に関する回答Yes! This is completely fine however, it is good practice to have the same brand of RAM sticks if possible.
"Screws to remove the Battery?"に関する回答No, there are no screws that you need to remove before taking out the battery. However, there are some screws under the battery that need to be removed to access other components.
"Using laptop after removing RAM"に関する回答You can still use your laptop as long as there is at least one stick left. If there is absolutely no RAM installed your computer will not boot.