What screwdriver size is needed for MacBook Pro mid 2012 back cover? What screwdriver size is needed for MacBook Pro mid 2012 back cover?

According to iFixit's teardown the Philips #00 should be used for the "lower case". Is the lower case a synonym for the "back cover"?
Yes.
The back cover is secured with Philips #00 screws.
Note that is says:

The lower case is secured by ten Phillips #00 screws.

You can see the ten screws on the back cover:

four each at the top/bottom
one each on the left/right