No. You need to be lvl 50 at least. It would be disastrous otherwise. You wouldn't have any skill points, morphed skills or anything. You'd have CP if you're a long time player. But for new players it would be constant one-shots and frustration.
I don't think so, vet dungeon will apparently work exactly as vet version of the DLC dungeon. And these dungeons cannot be done in vet mode by a player under the level 50.
From how I understand it, you can enter "easy mode" versions of the current vet dungeons, to explore the story before reaching level 50. But veteran difficulty requires you to be level 50.