Why can’t this loop be routed?

[1111F11]

And sometimes the path is planned but the vehicle does not move.

[maxime-clem]

It is hard to say what could be the issue. In general Autoware do not support loops. If a goal is set behind ego but on the same lanelet, then autonomous driving may not be possible.

From the last picture, it is not obvious why the vehicle does not move. Can you share the log file to see if any useful error message is printed ?
A possible issue is that the generated parking maneuver does not fit in the parking area. If you make it bigger does the parking succeeds ?