I think that they will link all the rainbow connection cliffhangers (like rainbow dash and rarity with rainbow in their eyes and the rainbow thread and what ever comes in the future. It is pretty obvious by now that every character is going to experience the rainbow eyes) to not what is inside the box, but how to open it. What is a big thing with a lot of story tellers? It's about the journey not the destination. If it all linked into what's in the box they will probably just open the box with actual keys, making the journey very uninteresting and I find this very unlikely, unless the rainbow connection somehow makes the keys, because it would be a boring story arc. think about it they will probably have to find 1 or 2 keys on the last episode or they would just open the box before the end episode(s), completely ruining the mystery and if they have to find the last key, it would just be a overly simple and maybe boring episode of them going on a journey to find something for the millionth time which would most likely end up with one of the mane 6 or more leaving the group (purposefully or non-purposefully) just like almost every adventure they have gone on to find something.
The rainbow connection could be linked to the episode where they realised they were friends before they met due to rainbow dash'a first sonic rainboom (the name of the episode eludes me at the moment) . Pretty unlikely though.
I also think the disaster will probably happen at the equestria games as it is a major event and the 2 story arcs are happening at the same time. However the equestria games story arc appears to have more focus at the moment, so it could just be a mid season story arc that ends half way into the season. However the Equestria games story arc could finish at the same time as the box story arc and they are focusing in the Equestria games story arc to reinforce my point about it not being about the destination, but it being about the journey.
As for what's inside the box I honestly don't have a clue. It could be the long lost heirloom for the equestria games, it could be the sword of holy titans, it could be more elements, it could e seeds to plant more trees of harmony, it could be an evil spirit, it could be absolutely any thing, or absolutely nothing.
This is all speculation though. Figuring this stuff out always interest me so I will be doing more digging tomorrow after school
NOTE: I don't think they will link flutterbat into the last episode because it seems like a completely different story arc IMO. Unless the cure her and that's how fluttershy experiences her "rainbow connection"
Also, what I want to happen is inside the box is a magical field that causes fluttershy to enter have her third and final transformation (her final form if you will). then flutterhulk and flutterbat to merge and kick some evil ass thousand year old dragon and have the children of the night help her. That's just what I want though
Also, please forgive any gramma and spelling mistakes as I am writing this at 1am and on my ipad and I was trying to get all my ideas onto the page before I forgot them, I still forgot a few points that, If I remember, I will update it.