Yes you are right, i see it as a currency, and i see NFTs as assets.
With staking, i would say: we can! The staking is perfectly fits in the equation. Just like here, with more HP you are able to make even more. I don't say money lay eggs on its own, you have to use it to get more.
NFTs are cryptos. Tokenization on the blockchains, whether stable coins or NFTs are all cryptos, which is why seeing crypto as a currency is only half the story. Yes, cryptos can be currencies, but that is only part of their usecase.
No, we can't. We can potentially collect more from what is available, but there will only ever be 21,000,000 Bitcoin printed. We cannot make more. What we can do is introduce different tokens and add value to those however and we can now do this globally with no central backing, which is valuable.
You are not making more HIVE though, you are collecting more for yourself to add to your stack. The equations for how much is in the pool doesn't change.