Answer to "Mixing different types of RAM"Yes! This is completely fine however, it is good practice to have the same brand of RAM sticks if possible.
Answer to "Screws to remove the Battery?"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.
Answer to "Using laptop after removing RAM"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.