I'm afraid your results are a bit skewed because Lucas' dtilt is one of the most unique trip moves in the game, in that it trips from 0-999%, and that it is location-dependant (it only trips with the tip of his foot). In the first test, you never tripped till the 9th kick because it took 8 kicks to push Sonic far enough away. In the third test, Sonic's higher damage pushed him into trip range faster.
The second test surprises me, because as far as I'm aware, there are no general mechanics in Brawl that are time-dependent. I know stale moves aren't. So, my guess is that you would've gotten the same results if you'd attacked again after 2 seconds, or 30 seconds. I think that when you stopped your continuous barrage of dtilts, Sonic had the chance to put both feet back on the ground again, which moved his hitbox forward a bit. I'll test this out though.
As for Non-lucas trip moves, each has its own range of knockback over which it can cause trip, which depends on the move's staleness, the target's percentage and weight, and the slope they're standing on. For example, Pit's ftilt can trip a bowser on level ground from 19-24% (training mode). I believe that once the conditions for a trip are satisfied, there's nothing that affects the probability of a trip. In fact, probability seems oddly uniform, even between different moves... it looks like they have either a 10% trip rate, or a 50% trip rate (Lucas' may be above that, though).
I did a big thread about this with a list of trip moves here.