The poster above pointed out the lack of a Soul Crystal. While you should have these after level 30, I disagree that it's necessarily a problem - gear is the most important factor. Looking at your character, you are actually a level 90 Dragoon while your Archer is level 13.

I actually had the same issue as you, so I know what you mean. I failed the duty the first time (and I've played for 9 years and beat lots of savage raids for context).

On my first attempt, I spread my damage across different orbs without actually killing them (I had lower damage due to being a tank). I was a melee job like you. I spread my damage across different orbs so I could avoid the AoEs.

On my second attempt, I killed one orb at a time. If an AoE appeared in the way, I just used my ranged attack from a distance (in your case as a Dragoon, this is Piercing Talon). This succeeded.

The reason it likely worked on my second attempt is that each orb builds the meter on your screen. So if you kill 1 at a time, it reduces the rate at which it builds. If you spread your damage across different orbs, all the orbs remain alive for ages and contribute to the meter. The result is it builds fast and kills you.

So this is either an easy mechanic or a hard mechanic depending on how you approached it and that's why some people find it difficult and others not.

To answer your questions, yes you can buy an MSQ skip book from the mog station. This skips the entire story up to the beginning of Endwalker (they're also on sale now I think). You can replay the story after this in chapters, but you can't choose the specific point you start at. The chapters are like the first quarter of the expansion, second quarter of the expansion, up to the fourth quarter. No, I don't believe a GM would play it for you or assist you with that.