Your first video shows the drivetrain working normally, but the second shows the "lockup". Were these videos taken at different times?

I don't see a freewheel problem in your second video. You are able to put tension on the chain and the freewheel has locked to the hub through its pawls. It appears that the wheel itself is preventing proper operation.
Are your brakes on? Is the axle mounted so that the tire is centered between the stays (and not rubbing). This looks ok in the video but we can only see one side. I also don't see much of a bottom bracket issue - if you can spin the crank backwards it can clearly spin forwards.

Check your brakes and how your wheel is mounted.