I think there's a slight difference between 'I lost track of the time' and 'I lost track of time'. The first means that I was so engrossed in whatever I was doing that I didn't know whether it was two, three or four o' clock. I had no idea what the time was. The second refers to 'time' as a concept - minutes and hours flying by. I was so engrossed in whatever I was doing that I had no idea how much time had passed. Obviously, they amount to the same thing, but the angle is slightly different. I think you could say either.

Yes to both questions. You could also say "Time ran away from me," which is something that is occasionally said (but it is much less frequent than "I lost track of time." Another thing which people often say in an office, in a bid to convince their colleagues that they have been working really hard is: "Where has the time gone?" or even (as a purely rhetorical question) "Is that the time?"