Is it possible that mine Hype tokens? If yes, which algorithm does it use?
It's not a mineable token.
However, new tokens are generated in the form of 'freezing rewards'.
You can do so by freezing your tokens. Which is a requirement when it comes to voting for the token's inflationary & deflationary rates.
More details can be found on the whitepaper itself:
https://hypetoken.io/whitepaper/