No on Rust it's an all out pvp server with no ability for parties or team system (yet) as it's still in alpha. So you can kill others and friends. If you and you're friends make a base make multiple entrances because the person that sets the door is the only one that can open it. I'll link some videos on it later that are pretty good lets plays on it.
Yeah I've seen some of DayZ. Kinda like another game called Nether.