Does SN (or its devs) know who tips who (amounts, time of tipping, etc)?
Yes.
Does SN know when I am logged in?
Yes, roughly. We know when you last visited as a certain nym, but we don't know if you're logged in/out otherwise. e.g. we can see that someone last visited a week ago but we don't know if they've logged out or simply haven't returned.
Does SN know when I log out of my main account and log into a throw-away account?
No. We don't do any cross-account tracking. Alt with abandon.
Related, does IP get tracked?
No, we do not store IPs, certainly don't track them, and never associate them with your account. But, importantly, your IP could be logged by things outside of our control or by tools that we aren't aware of. I recommend using a VPN if your IP address is sensitive.
I think reading somewhere that SN follows a stateless approach, but I am not fully sure what this means other than that the server does not retain any information about the user's interactions between different requests. Would this imply that the answer to all my questions is no?
Our authentication uses stateless tokens, which is what I think this is getting at, but we do store your posts/comments/etc (ie state) for obvious reasons.