Strange things with my 370Z

Arc

I park outside, facing towards the house. The car was locked and secured for the night.

Incident 3, today:
This morning when I walked out to my car, I saw that both windows were not up.
At first, I thought someone broke both windows, but I didn't see glass shatter anywhere.
When I checked, I saw that both windows had been rolled all the way down.
What caused this to happen? Sorry if this has been discussed elsewhere.
Should I take it to the dealership? Would they know what to do so that this doesn't happen again?
The car was outside, and I have no idea when the windows rolled down and for how long, but I found a dead spider and cobwebs inside.

Incident 2:
A few weeks ago, when I got into the car, I also saw that the center storage door was open and so was the passenger side glove box compartment.
The car had been sitting for over a week and no one entered the car, yet these two compartments were opened? Would some strong vibration cause these two doors to open by themselves?

Incident 1?:
My 370Z shipped just days after the horrible Japan tsunami hit in March 2011.
I had the car in the garage. While the car was off, I sat in the driver seat and inspected the interior. I noticed out of the corner of my eye, in the side view mirror, I saw a shadow figure walk behind the 370Z. This happened twice and freaked me out a little.

Now, no one has access to my 370Z and I keep a FOB with me and hid the other one so no one can have access to the 370Z.

Anyone have strange things like this happen to their 370Z?