Sounds rude to me. Not asking? Bad. Last beer? Worse.
The last beer is a no-no. I used to work with a guy who would bum cigarettes, and if I said, “No, it’s my last one,” he would say, “That’s ok, I only need one.”
Ask first. My reply will always be “Help yourself!”
I wouldn’t grab the last beer myself, if I noticed. However I would be pleased that someone felt so “at home” they they took my last beer. Most people who know me know that I don’t offer food or drinks unless I am eating or drinking but I expect them to feel free to help themselves to stuff just as if they lived there.
Most definitely.
Never take without asking first.
Never take the last one.
Rarely does anyone come to my place with no beer (I Might add it is rare they visit anyway 
). But I always have plenty in the fridge. I would not expect a guest to help themselves though- and NEVER the last one. You may have been saving that for when you got home. Or the next morning.