Nope, and Nope. The medals are not able to do anything other then be stored or consumed.
There is only one way to get premium boxes, by having a premium account. So yes, they're the same for everyone, for the most part.
Before this event started, you could save those premium boxes [as most max level players do since everything in the boxes is useless for a max level player,you only get premium for storage + Energy purposes] Anyway, saving the boxes was for when these events came around. You'd have a higher chance at getting a copy of the event item contained in them. I verified this with Leonis and Genesis personally before this event started.
Having had that knowledge and already having had saved some boxes, I then decided the best action, was to siply never use my boxes until an event came around worthy of using them.
Then this event happened. Leonis introduced new "event" boxes. These boxes are given to premium members in place of the normal ones. Making all those other boxes I and many others saved, well, garbage. They really hold no actual value with the exception of maybe 1 neptu every 30 boxes, and maybe a re-roll hammer or two.
After this event, I'll no longer be using premium. Specifically because it was told, by several people, that saving the boxes could reward the event items, then was switched [I verified this 2 months ago].
The decision was based on people going to extremes. Having 5+ premium accounts for months upon months. Farming several hundred if not thousands. Yes, this can be exploited. If by exploited you consider someone PAYING MONEY to do so. Granted, it is also probably "not what was intended", it doesn't change the fact. Having spent a significant amount of money, into a system that was verified to be true, only to have it changed the day of the event, when I could have invested that 60$'s into something else is the veritable straw.
After this development, all i can say is
Good luck. Might see you from time to time in TG, but game over.