Reading data streams of the 2 RX channels simultaneusly?

Yes, you are correct. LMS_SetupStream determines which channels are going to be used, and actually the first call to LMS_StartStream starts them all, subsequent calls to other LMS_StartStream is just for reference count tracking.
Rx streams started this way are timestamp aligned, not sure about phase alignment 2RX Phase measuremen issue -180 degree phase jump, I haven’t tried it myself.
As long as you read equal amount of samples from both channels they will stay aligned (as long as you’re processing samples faster than they are produced).