1. It most likely can. They are probably hoping to not bother the FCC by treating it as "test equipment" (that's what Ettus Research does), leaving the responsibility of compliance with the end-user.
1b. I doubt they're getting as much as a Watt out of that board (personal estimate would be a peak of 10-50mW, [10-17 dBm]) so in ideal conditions, significantly less power than a cell phone or wifi signal. Still enough to be trouble in some bands, and it doesn't change the regulatory situation.
2. There is an FPGA, so there is a physical possibility. It's not a trivial thing though, and working with FPGAs is even more remote from what most programmers are used to than working with GPUs. If I had to guess, the plan would be to capture/transmit bursts, with processing in between, instead of real-time signal/protocol shifting.