Yes, "hyper pull" work seamlessly with any Docker registry, public or private.
For persistent workload, Hyper_ provides the EBS-like volume, e.g. "hyper run -v vol:/path", but the volume is not local, instead it is distributed and replicated. And similar to EBS, you can create snapshots and restore to new volumes.
I think the website states it well:"Say goodbye to VMs
Unlike traditional IaaS where containers run in VMs, you will only work with containers in HYPER_. However, containers are protected by hardware-enforced isolation, meaning that they are as secure as a VM."
Does it connect easily with Docker Hub?
And what about running databases? How would I do that so that I don't loose any data?