the "must be asleep" condition is meant to keep the Langoliers out of the presentLacking a vehicle of their own, or arms in which to carry sleeping ones, there's no way they can possibly travel through the rip unconsious.
While their job appears to be eating the past, the Langoliers appear to be attracted to things from an "active" timeline.Note how quickly they home in on Toomy and the plane when they arrive. Yes, they're eating everything along the way, but they take a special side-trip to munch on Toomy and the airport where he'd been, and then try to take out the plane.
Toomy's father genuinely knew about the Langoliers, but he only knew half the story.Every legend starts with a grain of truth. Toomy Sr. might have known about these creatures that ate the past (by some means; this is the King-verse, after all), but he interpreted that to mean they ate up people who wasted time. Keep moving forward in time, don't get left behind, and they won't eat you up.
The entire purpose of the dead past is to provide Langolier-food....as opposed to saying the entire purpose of the Langoliers is to eat the past. These are eternally-hungry eldritch abominations, and they must eat something - more to the point, they must eat everything. If Some Force didn't keep the dead past around for them to eat, they might catch up with our active timeline (see above) and start eating that, and we'd all be boned. It just so happens that time keeps moving forward, leaving dead time behind, just fast enough that they never catch up.
Toomy Sr. did this before.How else would he know about the Langoliers. He seemed genuinely scared for young Craig's life rather than simply delusional. Who knows, he and a couple friends have probably went back in time, and witnessed it barely escaping with their lives. His warped mind from the experience led him to believe that they constantly follow those that stay still until the active timeline becomes dead past.