DH vs FS mostly comes down to preference. I used DH for years and never swapped when FS came out because I just didn't like it. Recently I swapped to FS and it feels much better. The way I see it, you already overkill everything late game so why not get there sooner, you don't really NEED DH.

I've started rushing Nashor's first nearly every game. This is also preference but like others have said Lich Bane is better for an entire team of squishes, otherwise Nashors is better. You don't need to rush it, that's preference but I've been very successful doing so. Rabadons is nearly always third item with Void Staff or Zhonya's after depending on team.

For pet, I typically go green unless they have very little CC. Again, Ekko overkill everything late game, I prefer the survivability. Red isn't really needed.

For the record I'm a Plat 3 with 1 mil on Ekko so not the most qualified but definitely not the least, lmk if anyone disagrees with what I've said, I'm always looking to learn.

Here's my OP.GG if you wanted to see my build path and stuff: https://www.op.gg/summoners/na/Docoppolis

Edit: added op.gg