In my opinion, ki is just a different way of explaining proper technique to an aikido student. When your mind, body, and spirit are in alignment, that usually means that the bones in your hand are in proper alignment too. Personally, as an assistant instructor, I've had more success telling people how to extend their ki, than trying to explain physics and body mechanics to them.
Karateka have a better chance of sending that hand through a board if their mind, their intent, is on the other side. People can study our movements with slow motion photography and attribute everything we do to physics and body mechanics, but when I'm in the middle of randori I don't have time to think about it that in-depth...
...so I just extend my ki.
As for "feeling" an attack coming, I think that the original poster's sensei could have used different words to get his student to concentrate on the impending attack. When we still our bodies and our minds, when we stop all that blasted thinking, we open ourselves up to other things. It could be explained by something as simple as hearing their foot leave the mat, or a quick intake of breath when they step in to strike; Maybe it could be something different, something more. I don't know. The minute that I say I do know
, the minute that I close my mind to possibilities, my aikido will suffer. Good luck to all of you.