1) Taxes? I believe I mentioned that. They're kind of a key feature of any government function.
2) I'm well aware of how far $10k doesn't stretch, since I live on less than that. I'm on SSI. To get by, I have to live with my mother, also on SSI, and my grandmother, retired. But I do get by. It is normal for people of low-income to cooperate in this fashion, and I'd hope it would be seen as even more normal in the near future, considering that automation is about to collapse the labor market. Maybe someday it'll be normal enough that you can still get a date if you have to do it!
3) They don't. But it's better to have $10k than to not have it. I was homeless in Seattle for a little while. There was a very clear divide between me and other homeless people: I had money and they didn't. I wasn't completely reliable on the shelter system for food. I could replace my socks if I needed to. I didn't have to schedule showers a week in advance, because I got a gym membership when they were on sale. $10k isn't enough to be comfortable, but it is enough to stay alive and sometimes even be human.
As for salaries and infrastructure: there wouldn't need to be any. The entire point of UBI is that first letter: universal. The total cost of a program where everyone, regardless of need or demographic, just gets some money is about 0.1% more than the actual money doled out by it. All you need is to verify a person's identity and whether they're alive or not. We already do that for a bunch of other stuff. Just use the existing infrastructure.
"And what the fuck will happen to world politics when the US completely defunds its military?"
Uhh, I dunno. What the fuck will happen to your argument when you explain what that has to do with anything?