Here's a good interview which clarifies some details. Almost.
Sounds like PVP will be kinda-sorta opt-in, or at least balanced in such a way to prevent griefing and/or incentivize good behaviour, but who knows how this'll work in practice. Definitely something they're still working on. They want a little drama without the assholery, so maybe this'll hash-out way more like Sea of Thieves instead of Rust.
Private servers are implied, and fully moddable private servers seems to be a post-launch goal. Hell, I'd be happy just to have private vanilla servers, I think, even if it's just an option to use in a worst-case scenario, like if every single populated server is full of shitheads.