All hardware is theirs, you rent it. They repair it when it fails at no cost, but they don't monitor everything (althought some come with agent to install on dedicated server that passes monitoring data to their system).
So if you say see SMART errors on hard drive you have to open ticket with them to fix.
> What happens when storage fail? Are data backupped or it is on me to make them?
You have full control over server. If you want backup you need to set it up yourself.
I'd start with VM if you want to learn ops stuff. Those also usually have backup option at some extra cost.
kimsufi (ovh brand) also have some cheap ones, I have some atom serwer with TB drive for some offsite backups and few services and so far no problems.