The core is just the engine, i.e. the server software. The code. I'm guessing theirs is a heavily modified MaNGOS. To create a server, you download some packaged stock core which is the databases, scripts, mechanics etc. Then you modify it to your liking, and when servers talk about having a "good core" then it means they've fixed bugs and scripts and whatnot to improve the quality because stock cores are crap.
There should be no reason to limit the PvE server to 2500 players unless you just don't want it to be too crowded. Given the fact that it's a PvE server, it doesn't make sense to go to such lengths to avoid crowding when they didn't do that for the PvP server where crowding leads to real issues as people can't play properly due to constant ganks and an excess of bored 60s griefing lowbies.
At launch everyone will want on, and without a cap it would be horrible to level if not impossible.
The PvP server was clocking something like 7k players at release, and while it was definitely crowded and annoying, it wasn't impossible to level. Certain quests weren't really worth doing, like ones where you had to pick stuff off the ground when there's thirty people trying to do it. Then you just had to grind mobs for a bit or something to compensate for missing out on that quest.