It really depends on who you ask, I suppose. Thanks to Rhombus, I recently started watching the TV series, and have come up with a few conclusions of my own regarding dinosaur beliefs.
-Flyers clearly have their sun-worshiping system. That's an indisputable fact, at least in the Great Valley
-Longnecks seem to be religious, hold the stars in high regard, and have a rich history of folktales
-Threehorns are pretty much atheistic
-Most other leaf eaters tend to fall into one of the three previous camps
-Sharpteeth are a mystery, so I took some creative liberties with them. In this universe, they seem to oppose the idea of deities, but many like Rear value nature as a great being in and of itself.
-Sol's an interesting case due to his early abandonment. As a child, he would have been told scary stories about spirits, ghosts, things that go bump in the night, etc, but I never saw the Longclaws as having a belief system of their own (except possibly worshiping the river, their source of life, in some circumstances). Because of this, Sol grew up retaining his childhood beliefs, but as is soon to become evident, this lack of faith leads to a bit of a dilemma for someone who wants something to believe in, like his Longneck friends.
As for the time skip, there have been a few references to it throughout the story. It's implied that they left the Grove during the end of summer of the previous year. They met Cera in the fall and stayed with her through about half of winter. The journey to the scar is the longest time skip yet, taking them to the very beginning of Spring, so it's really a little over half a year.
Thanks as always for the insightful review, and I intend to put your points into consideration as the plot moves forward!