Hmm...I think you might be looking a bit too deeply for meaning in some of those scenes;
How Petrie escaped from the sharptooth
I doubt this is a missing scene; it's an old film cliche, a character making a miraculous escape at the last minute - same thing happens in Indiana Jones 3 when the tank goes off the cliff. You think Indy must have died, then without any indication how, he climbs up the side alive.
To speculate, Petrie's dripping wet when he climbs back up, so we know he got out when Sharptooth fell into the water. Come to think of it, the large rock falling onto Sharptooth's belly in the water probably knocked the wind out of Sharptooth, and as such caused him to loosen his grip on Petrie; who was forced to climb back up since he wouldn't be able to fly with wet wings.
Why Spike seems so big when he steps out of the grass
Why Petrie was a black flyer in his first moments onscreen
Nah, that'll just be a continuity error - more likely, the animators intentionally sized Spike up quickly lest he be very tiny for the whole film. As for Petrie being black in his first appearance, it's more likely they intentionally did that so it wasn't clear what Petrie was when he fell on Littlefoot, so he could seem scary, and then be "unmasked" (alternatively, it is an old cartoon; and the colours aren't always consistent).
Why Petrie was left behind
You might as well ask why/how Ducky or Spike were left behind. We don't need to know; Ducky sums up that she "lost her family in the big earthshake", and that's all we need to know; we can assume the same applies for the others. It is odd that Petrie's mother wouldn't come looking for him, but this is probably just a mistake in the story that nobody thought about.
When you consider all of the parents on the other side effectively abandoned their kids and continued on to the Valley, it's likely that she thought he was dead (we know they were working together not long afterwards; why didn't they get the flyers of the group to go across the divide and search for their lost kids?). In fact, I think there was a post about this somewhere else; I know I speculated he could have fallen from his nest in the earthshake and become lost, and his mother could have returned after the earthshake and failed to find him, and was forced to move on, meaning that by the time Petrie found his way back to his nest - the tree - he had little other option but to climb it and hope his mother would come back.
What happened to Petrie's dad
Since he's never mentioned in the story at all, I doubt he was ever meant to be a character. It was probably just an idea someone came up with that he didn't have a father at the end. Besides, the only way you could work this in without having a scene at the end where his mother tells him his father is dead would be for him to have died during the earthquake; perhaps protecting Petrie. But there's no indication for this in the story or the soundtrack, it would add little to Petrie's character and it takes away from the emotional impact of the death of Littlefoot's mother.
How they escaped from the tar
There could have been a scene for this, but there's no indication for it in the music - this bit is the same on the CD and in the film. Besides, it's likely that it's intentional; to show the characters escaping from the tar means the audience doesn't get the emotion of shock when the "Tar Monster" arrives and is then revealed to be the main characters.
How Littlefoot and his mom got seperated in the earthshake
Hmm...that is an odd one, but again, there's no indication for it in the music. And besides, why would they have cut this or a scene where they get out of the tar? We know they only cut scenes considered too disturbing (and potentially that bit in the story with the two racist groups of duckbills); what would either of these scenes have done to warrant a cut? Likely the audience is just meant to think they got additionally scattered when the earthquake continued.
and, of course, what happened to Cera's mom and sisters.
I don't think this was a scene in the original film; for one, where would it fit in to the story? They'd either have to show part of the parents' journey (which wouldn't suit the film's story), show them dying in the Earthquake (which we know didn't happen) or being found dead later on (which would have changed the last scenes of the film completely), or awkwardly work in a line when Cera finds her father, which would have killed the scene.
I think we can blame the sequels for this one. It's not said in the original film that any of Cera's family are dead; we simply only see her reuniting with her father (with another Threehorn visible nearby when we cut to Littlefoot), and so it could be that when the second film was made, the story-writers didn't bother to work Cera's mother (aside from potentially a brief cameo when the parents rush to rescue them from drowning) or siblings (again, also potentially shown at the ending), and by the time the third film came around, they decided to abandon those characters completely and continue without explanation. Compare how Ducky's father vanishes after the fifth film; presumably since he didn't add anything to the story, the storywriters decided to drop him and make Ducky's mother a solo parent (then the fans come along and conclude he could have died on the way back to the Valley after the events of the fifth film).
