1: The higher your Mayhem, the stronger the weapons that drop. Just farm whatever boss you can easily kill even on higher difficulties and you are bound to pick up some good stuff along the way.
2: No, but it certainly helps. Some of the top tier weapons in the game are DLC based. However, I’d say you are somewhat lucky in that you are playing Amara because she doesn’t really rely on DLC stuff that much. If you were playing Zane, I’d say you kind of need it because his best and easiest legendary class mod is tied to the Handsome Jackpot DLC.
3: Not much of an Amara player, however I will agree with other posters here that Lazydata has some great builds.