Hello Torsten,
"Problem 1. ... When I go into the test activity again and change something else like the name, the tick in "Or all available attempts completed" gets removed."
This is probably due to the fact that the activity has already been marked as completed for some participants. Changing completion options would erase their completion state and may cause confusion. Thus the completion options have been locked and should not be unlocked unless absolutely necessary.
In other words, although the tick in "Or all available attempts completed" is removed, the completion options have been locked and "Or all the available attempts completed" is still active.