Can thickness be given to a plane?

Yes, so many ways to give thickness to a Plane the easies would be using Shell Modifier or face extrude using Editable Poly

YES

USE SHELL MODIFIER

I think everyone have their own ways to work with diffrent softwares, If it was me, deppending on a situation I would convert int to a poly and then do what ever I need to do...

Yes... Just Apply Shell Modifier...