Can a cop pull you over walking home asking why you are out so late?

Sure they can. It happened to me a few years ago.

I was going back home from my office, around 3 or 4 am. Huge project to hand in, I just kept on going until I had it finished and polished, and when I finally managed to finish I drove back and started looking for a parking spot.

That's when the policemen spotted me: I was so tired I was unable to park where I found a spot, and just drove to the next one I found. When I left my car, they pulled me over and asked me a bunch of questions (the usual ones, like where I was going, where I was earlier, etc).

Have your parents ever walked in on you?

I was polite throughout the whole interaction, there wasn't much they could do. They weren't nice until it was clear I was just tired and not DUI, but that makes some sense.

I told them I was in the office. They asked if I'd been drinking. I told them I was just too tired to park properly and wanted to go to bed. They kept asking dumb questions about my job (I was so tired I’m pretty sure I was really confusing), so they gave me a breathalyzer test, and then let me go once they understood they were just bothering a poor person working too many hours.

Uhm, just as a note: Europe, not US.

Gun owners, imagine if an attacker comes to your home and takes your gun to use against you before you had the chance to pick it up. Would you regret owning a gun?