Is it worth getting the icon and border?
Depends on if you'll use it/them.
Will the border ever expire or go away?
The borders only work for Project Jhin, Project Vi, and Project Vayne.
If you don't select one of those three in-game it won't work.
If you plan to buy them at a later date, the border will apply to them then.
Or should I test my RNG with project orbs or shards?
Up to you really^^
Just want clarification on what the top reward actually gives.
It gives the Final Hunt summoner icon and (upon owing Project Vayne, Vi, or Jhin) it will put a border on them in the loading screen.