HSA: 1. do you need to hold any amount as cash in the account or can you invest all of it? 2. do you need to have a HDHP? OR can you contribute to a personal HSA if you have no insurance at all?

For number 1, that depends on your HSA custodian. Some require some minimum amount to be held in cash and others don't

Seems you need a HDHP to be able to contribute to an HSA.