If someone leaves the party during in a dungeon, the rest of the party is queued in dungeon finder again. When a new player is found and added to the group (say I am that player), is it possible that I can directly get to the group rather than the dungeon entrance and run all the way up? It's a long way to run at least, and if the monsters are respawned, it's impossible to pass on my own.
I am pretty sure that trash still has a re-spawn timer. However it is usually 2+ hours and it is often tied to bosses. Therefore if you kill a boss post trash, that trash will no longer be able to spawn.
In dungeons these days, the chance of a 2 hour + run are minuscule, so it just isn't seen any more.
It might appear that trash re-spawns, however it is more likely that this trash pack has been skipped by the group. Players run dungeons differently, take alternate routes, skip patrolling trash packs etc, so for a new player, it can certainly catch you out.
Regarding teleporting to a dungeon in progress. I am not 100% sure of how it works, but you sometimes will get teleported directly to the party mid dungeon.
Some factors which might decide why you get teleported to the start or the party could be:
Unfortunately I cannot confirm or deny the above, but just trying to give you a few potential reasons why you don't always teleport to the group and instead go to the instance portal.
Hope that helps.