No, the new terminal and the intermodal facility are parts of the same complex. There will be a short skywalk.
It's a 4-minute ride on a modern, speedy people mover. Direct, non-stop. Actually, quite a pleasant and scenic ride. No more hassle than riding an elevator.
IIRC, Brightline does screen passengers & carry-ons at its stations. But it's a simple walk thru a metal detector at the ticket check, and carry-ons thru an X-ray belt. No elaborate rigamarole like TSA.
Brightline handles checked baggage at its current stations. If the company decides to provide service between MCO & WDW (which at this time is unknown), and if the WDW station is built to handle checked baggage, hand-off directly from the airlines to Brightline would likely be available.
If the service is provided by SunRail (which is another possibility), there will be no checked baggage (unless Disney provides the service separately), but also no screening under the current model.