Yep all the Surface keyboards are functionally interchangeable, same connector, same interface. Except the Power function of the Power Cover doesn't work on the Surface RT.
Logitech Bluetooth keyboard??? TBH I'm not a big Bluetooth fan but a lot of people use them.
MS just released a new universal BT keyboard. FWIW.
The type 2 will definitely work on the SP1. To be honest I'm a bit worried too about durability of the covers as I've gone through two replacements on my power cover already. Warranty service is awesome from Microsoft but that's only for a year.