Is this true? Bunnys travel long distance with these standards?

Well, they are true, but some can be modified. It's common sense not to leave ANY animal in the car on a hot day. We used air conditioning when we were traveling and the rabbits were fine. In general, rabbits do better in cold weather than they do in hot. You don't need to establish a routine while traveling, and you don't need to strap down the carriers. Just put them near bags and things so they do not move around too much. At night we brought the rabbits into hotel rooms and fed and watered them. They would get water on all the stops. They did eat hay while we were driving. If you don't have one already, get a rabbit carrier. They hold a few rabbits and have very small separated compartments that help the rabbits from sliding around.