is there any chance of being hacked on Facebook while using virtual private network? and can the provider use my account for any unfair means?
No. Your connection to Facebook is not at risk when you use a VPN. That's because the communication between you and Facebook is SSL-encrypted and therefore the content cannot be read or modified by anyone in between, neither your ISP nor your VPN provider.
They can conclude that you use Facebook but not read or control what you do on Facebook.