I want to know if running a tor hidden service also creates a relay/node. I want to know this because my vps provider bans tor nodes.
No, running a hidden service requires very little, not even an open port, you can do it with purely outbound requests.
Yes, generally, but it's not a requirement. You better have 1-2-3 different relays running 24/7/365 to use as a bridge or entries for your HS host - it will improve it's visibility and speed greatly. Strictly and minimalistically speaking - no, just an instance of Tor able to connect to the network is minimal-enough.
Single word answer for your question: no.