Borderlands – Is it Possible to Access the Loot Chests in Marcus’ Bank in the Underdome Riot DLC in Borderlands 1

I can't say for sure, but I would guess it won't allow you to play.

Character information is most likely stored in the game save, which was probably altered somehow by the DLC, so I guess a game without the DLC won't be able to read it properly.

I would test it for a more "official" answer, but I don't own the game.

Its worth doing if you want the skill point as reward at the end of the quest. As for doing them solo, I know its fairly easy to do on Hell-Burbia as there's a spot you can jump up to (above the stack of crates) where the enemies cannot reach you. As long as you have a class mod that regenerates whatever ammo you use (I prefer sniper rifles in those situations), you'll be fine.

The Angelic Ruins and Gully don't have easy hiding spots so it entirely depends on what character you have but its much more difficult to solo due to the different enemies that spawn in those areas (I have never had the patience to fully attempt either one to completion with any of my characters).

I would suggest joining a game with another character who's at much lower level than you, as the enemies will be scaled to fit their level and then you'll have a much easier time to complete the missions.