How are you trying to close the hatch - the button on the dash or remote will not close the hatch (in the US only) and you have to manually close it or push the button on the bottom of the actual hatch to close it. If you pushing the button on the hatch to close it and it isn't working, then it is broken.

As for the oil, should not leak any, but it isn't uncommon that they spill some when they change it, and it may have been recently changed, so I would take a look underneath, clean any off and see if it comes back indicating a leak.

Your mats should have the disks screwed into the floor, someone just must have lost them before you.

4 does sound like a power cord for a radar detector, pic would help, but based on the placement, sounds like the obvious answer.