The US is monetarily sovereign and can always issue enough currency to meet any demands upon it.
Yes. When congress appropriates funding and it’s signed into law, the effect is that the US Treasury spends that money into existence. The mechanism, of course, is that Treasury directs the fed to issue bonds to create the money, and when you pay taxes that money doesn’t go into an account Congress can spend from, it goes back to the fed to zero out the bonds used to create it.
Of course, if we continue cutting taxes the way we have, that will eventually balloon the amount of currency in circulation and that can be problematic if it’s untethered to reality