I'm thinking about getting an VPS to install OpenVPN on it to connect in a secure manner to the Internet from free Wi-Fi networks. My question is, what is the scope of my responsibility, to keep my VPS secured? If compromised, is there any chance, that an attacker can gain access to other VPS or basically the software/hardware that the company relies on, to deliver their VPS service? Can I be held responsible for this ?
In theory (and out of few exploit to gain host control) a VPS is isolated from others VPS.
If your VPS gets compromised and the attacker can compromise the host and other VPS, that should be the hosting provider matter as this mean a vulnerability inside the host hasn't been fixed properly. I said should as some providers will put the burden on the first compromised VPS, read carefully the contract.
Usually your VPS security is still your responsibility in all cases, if it gets compromised and is used to attack something, you'll be accountable for the use of this VPS in the attack.