That part is the cellular antenna. iPhone 5 Cellular Antenna

When re-inserting the #3 connector how much force does it take to get the connector fully inserted? How can I tell whether it is fully inserted?

I found a #0 Philips screwdriver worked better for removing these two screws

I suggest you also have a #0 Phillips screwdriver and a T7 Torx screwdriver

I found that a T7 Torx screwdriver worked better for removing the two hex screws

I found a #1 Philips screwdriver worked better for removing these two screws