Yes, because ordering someone who may have ZERO running background out onto the pavement OR a treadmill is safer for knee and joint health than an elliptical. If you're going to incorporate HIIT into an elliptical workout just don't try to bang the machine around, it forces momentum on your joints and completely messed with the human lower body power curve - I would echo what Mudvayne said - forget speed, go with high resistance and incline.

For elliptical, I say turn up resistance and incline levels. 60 sec intense and 30 sec rest, repeat for 3 sets:)

Yes to run as hard as you can, but at a controlled time. HIIT isn't meant to burn yourself out all the way. You don't come to the gym and do one set. You have to take "breaks." My advice, run hard for 20 sec, speed walk for a min, then run hard again for another 20 sec. Repeat for 5 cycles. Enjoy :)

I can't really see how an elliptical is inferior to say a stationary bike. You don't need to incorporate any of your core muscles (or any of your upper body at all for that matter). Either way... the resistance is where it's at. When doing the HIIT for 1 minute at a time I found myself cursing every word I could think of at the 30 second mark. That's typically the intensity your looking for. By the end of the minute your muscles should be begging for that rest period. If you still have anything left you need to go harder next round.

I do my HITT on the elliptical, here is what i do and it is very effective for my PM session when trying to lean out- I warm up 5min at a steady state, then 15sec burst (yes up the resistance) then recover 45sec(slower but keeping the resistance the same maybe half the effort), i do this for the next 20min and follow it with a 5min cool down. PS if you hold the hand grips and lean back, making sure to dig in with yoyr heels your glutes will BURN,like nothing else.