Blackheartsgirl I'm so sorry you're going through this. 
I don't know how much use anything I can say actually is to you, but I'm going to try saying it and hope...
No you're not stupid, you're overwhelmed by an overwhelming situation. It's a reasonable reaction to what's to hard to cope with for the vast majority of us.
Things you may still be able to do:
Remove notices if you haven't already.
Call the council, tell them what's going on, and that the cars owner is deceased, and you've been struggling to cope. Ask them to pause action.
If you can get the car moved to a different location, do. If it's possible to get it onto privately owned land with permission, absolutely do.
If you can't, put a notice on it explaining situation, it may not save you, but if you give contact details it just might buy a pause. (Also may not, but doing something generally gives us more peace)
Or if you have the money, or any friends who might do it for you, insure the car, and call council on Monday, and then send of for a replacement V5, and deal with it in your own time.
One last possibility is try and sell to gumtree type tow guys. With an MOT it's automatically of interest, even if at a low price. I realize you may not be able to cope with actioning this last suggestion.
I get the heartbreak of having to let go of his posesions, I really do.
(For what it's worth, in a few days time I have to send a vehicle with painful attachments through ownership to scrap and losing control of the situation is part of why. It all hurts like hell, and makes me want to scream in circles, but experiance has taught me that in the end this too will pass.)
If I laid out what's happened here, you'd be saying similar to me about overwhelm, not stupidity. We are human, and can only hold so many things together at the same time.
I'm going to say Well done on the tip run anyway.
Wanting to give up is beyond understandable, and it may be that tonight the best thing you can do is take time out (tbh it's when I get the alcohol out) and face tomorrow when it comes.