Law enforcement: Do plain clothes officers really stuff their firearm into the back of their pants like you see on TV?

SOME may use a holster in the back, but all real officers use a holster. That said, it would be more difficult to sit with a holster on your back than a side holster.

No.

No, that would be too difficult to keep the weapon in place and would violate my department policy.

Every plain clothes officer I've seen has a holster designed for plain clothes carry that must be approved by the department.