Are all rectangular outlets, switches, and plates the same dimensions and interchangeable?
Yes, all "Decora" style devices share the same cover plate opening, within a couple of thousandths of an inch (+/-.005" or so). GFCI receptacles also fit this description, as well as many dimmers, timers and "smart switches".

For instance the opening on a Hubbell plate is 1.312"x2.625", while these Leviton are slightly different, but all within a reasonable spec to be called the same.