Could have taken place quite some time after the fire. We never know how long those time gaps are after all. (Maybe that's why the call it the Land BEFORE time. Argggggh! dino_laugh.gif )
You are kind of right, minus it might be nice to see the first film.
Yep, yep, yep! It's kinda odd to watch a series without watching how it started... I remember I avoided the first movie as a kid and I have NO idea why... kinda regret I did 
However, the TV series seems to be the flip of that, as you'd have to see 1, 2, 3, 4, 5, 6, 7 (if you wondered who Pterano was), 8, 9, 10, 11 (if you wondered what a tinysaurus was), and 12 (13 was produced at the same time as the TV series ans so far, Loofah and Doofah don't make a reappearance, which is a pity as I found them adorable.) (12 to find out who Guido and Tricia are.)
Sure, there are references to earlier movies quite frequently (and particularly in the series). It's okay to like the Yellowbellies though there might be some people who hate them to the bone :unsure: Well, I didn't exactly like them but I can see why the writers created such characters.
If they finally addressed continuity in the TV series, I'm thinking that they will probably focus more on it in the upcoming films.
Of course, they've also created some continuity issues... We shall hope the possibly coming LBT 14 will try to stay true to the previous movies 
The death of mother longneck might have been the reason you didn't see it. I know I avoided Charlotte's Web for years after finding out she died at the end. In fact, even now, I'm not too keen on it because of that.
I have watched the first LBT movie and, in fact, have found that if Mama Longneck didn't die, it would so also the timeline that dozens of characters would die or have different destines.
(I can say, for short, that the Gang of Five would all have died, Ali might have died, Hyp would have died, Grandpa Longneck would have died, some herds might have died in V as they would have broken up, Tippy and his herd would have died, Mo would have died, Tricia would have died, Pterano would never have reformed, Shorty might have died, Mama Flyer and Skip would have died, Petrie's sibling would have been orphans, Ozzy and Strut would have gotten all their eggs, Swooper would have stayed in the Mysterious Beyond, the Great Hideous Beast would never have been defeated, had Ruby met Chomper, it would have been the last thing she ever did (as he would not have met Littlefoot and hence been a bad Sharptooth), and, based on that, Chomper would not have been there to save Mama Flyer from the mud, hence her death. I figured all of this since the others would have died in the Mountains that Burn as it was Littlefoot who saved them all and he'd have gone another way with Mama Longneck had she still been around and hence he'd have been the lone survivor of the Gang of Five. As he was alone, he'd never have crossed paths with Chomper, hence making Chomper be a regular Sharptooth, and also Littlefoot, Nod, and Mutt wouldn't have been able to save Hyp from that tar pit alone. Also, as there would have only be Ali to save Littlefoot in the fourth film, Littlefoot and Archie would have been made a meal of by Dil and Ichy. Also, if Ali later broke through the rocks, she'd have met the same fate.) Also, there are several characters who
wouldn't have died, among them, Sharptooth himself, as well as the Plated Sharptooth from the fifth film and the Mountain Sharptooth from the 8th film. All in all, her death makes the series possible.)
Also, one wonders greatly why Littlefoot didn't try and strange Chomper with those vines. Based on some a song from the beginning of Great Valley adventure, there appears to be not much time between the end of the original film and the start of that one. Given that he probably was still bummed out over losing his mother, and certainly knew what type had killed her, why didn't it ever cross his mind, when he laid eyes on Chomper "Yeah, he may look cute and innocent NOW, but when he's older, he could take someone's mother from him. I've GOT to end him!". Yeah, one may think, that's cold, and no character would do such a thing, despite their hurts. However, Ali's herd almost does just that in Brave Longneck Scheme. Is Littlefoot more moral than Ali's herd, including its leader?