Hi,
Can somebody please suggest me the possible options to setup content deployment between an on-premise SP 2013 site to an Internet site hosted on a separate farm on cloud? And the best practices.
I am pretty certain you can’t take a full site collection backup and restore it Office 365. You could have all manner of customisations and features that wouldn’t work in Office 365. You are probably better off looking for a 3rd part tool to do this for you.