Planetary Annihilation networking
The PA tech is actually a very mature tech that started with Supreme commander (The 10 hz update rate concept, with seperate loop running for animation/UI)
The simulation runs at 10 hz, everything else runs "normally". Things looks smooth because the part running "normally" renders the deltas for movements/turning etc. Also, the game is lockstepped, so you're see'ing the "past".
Keyframe creation is done as input is given that will change the simulation, if I understand it correctly.
Lockstepping in PA's case means that what you're see'ing is a few frames old, which is enough time for the simulation to solve the issues (for example, calculating deltas of movement of 2 units crashing into each other is resolved and sent as a keyframe of a collision, instead of that delta value rendering for you.
They're old on the client as well, however, the client is viewing older simulation data.
Lockstep networking solves all sync issues that you mention. The server only proceeds when all players are informed of what happened. The server then waits for that to render.
The situation where t=0.67 when the latest receipt from the server is t=0.5 shouldn't happen in the general case. The client will try to keep itself at the server time + the average latency + a bit extra. Most of the time you're playing you will be interpolating toward the latest receipt from the server. Occasionally with a network hiccup you might accidentally catchup and overtake, I don't know what they do in that case. Probably they allow a little bit of running ahead with extrapolation, but if you end up too far ahead the time on the client probably slows then stops so you're not seeing too much made up stuff.
This also answers questions 4, 5, and 6, I think.
Thanks for shedding some light into this. I guess that makes sense... if the client gets too far ahead of the server values, that's when you could start seeing strange behavior or harsh corrections.
For question 4, then I guess stopping could happen naturally when you've reached the endpoint of your curve (or the "not too far ahead" point).