Whiskey Foxtrot IS going to have his bursts stop being semi-auto. It’s slated for an upcoming patch, but I’m heading to work shortly, hopefully someone else can find the link for us.
As for loot chances: in Borderlands and BL2, adding more players increased the drop rate (because it also increased the difficulty.) I presumed the same thing was going on in Battleborn, and so far it does seem like you’re less likely to get legendaries from solo missions.
As for Advanced vs Normal mode … you’re definitely more likely to get legendaries from advanced. There’s also a larger pool of legendaries in advanced, as some of those won’t drop in normal. However, because the difficulty changes, some legendaries (I’m looking at you Vow of Zealous Fury) are much easier to get by running normal mode twice as many times in the same span vs running advanced and having a greater chance to fail the mission.