1. Yes, it's supposed to happen like that. Don't run all the way in, just keep fighting them and they'll stop spawning more after a little bit.
2. Yes, during your last quest there, Into the Pit, there is a pretty challenging fight against the Mutated Colicoid Broodmaster that you should look up to get some tips on how to beat it (the basic part to win that fight, though, is to kill the adds that spawn).
Overall, if your class quests seem a bit too challenging, just put them on hold and gain a level or two, then when you go back to them they'll be much easier (for example, finish Balmorra and the bonus series, then go back and squish those bugs like ants).
Edit: Also, anyone talking about leading the bugs down a hallway, or adds spawning on a timer, is referring to the Broodmaster fight from Into the Pit, and not the fight with the bugs that keep spawning (during Scientific Inquiry I think the quest is called). Just stay where you are, keep fighting those bugs, and they'll stop popping up eventually.