Glad to hear things are coming together for you. You can always respec your skill tree at the appearance change station. I highly recommend Longbow precisely because otherwise the turret dies so quickly otherwise. The most common approach to Axton is to aim for Double Up and Gemini at the end, so I’d expect that to look something like this at level 64. There’s some flexibility to shuffle points around. Several are there just to be boosted by COMs if you have them. My Axton has a blue Engineer COM boosting Sentry and Battlefront for example, while the point in Expertise is mostly in the hope of someday getting a Legendary Soldier COM. Some people recommend points in Forbearance since damage over time effects are pretty deadly in UVHM. Having Double Up is incredibly useful for the slag.
Grenade jumping is never necessary that I’m aware of. It can be helpful to bypass stuff - the place I’ve seen it most was in Saturn farming videos to just go straight there over the fence rather than fighting through Fyrestone. You’ll always want to remove your grenade mod before trying, of course. I haven’t seen rocket jumping in this game but I’d assume you’d want the lowest level possible, maybe a level 12 Duuurp or something.
I keep finding new stuff in this game, as do people who have played 10x longer than I have. Chances are that for any seemingly inaccessible chest, there’s another way there, perhaps going past it then working your way back behind, or finding a way to get above it and jump down, etc.