The loot/drop/roll system is tightly guarded information. There are guides that have been made and info on where to find vanities or legendaries.
Vanity info can be found by searching forum with the word vanity, you can search by the vanity name and find som specific info of where it drops
For legendaries, you can search with the words legendary or pink on this forum also. And you can search by the name of the item.

As far as the re roll enhancers, there is the 25% and the 100% miners. Miners will reroll 100% of the time to the next color loot, if that option is available on that map.
You could try searching this forum with the words loot, drop, reroll to get some info.

Vanities can't be rerolled. It would suggest they are on a seperate loot table from the others, possibly needing to hit a certain roll to bring out the vanity table, or possibly a vanity needs to be generated to the map when it gets populated with loot in order to have a shot. I am unsure of this mechanic.

No as far as the drop system. I don't know much. I was told to imagine dice, but with many many sides, the numbers are for the loot and what rolls is what you get.
A reroll at 25% , aproximately 1 out of 4 drops will get a reroll to a higher colored loot, IF it is available on that map to happen, an example is you won't be able to reroll a green from redsun to a purple, because purple is not on that map.
A 100% miners luck reroll will reroll every drop, but same thing. It WON'T reroll if a color up is not available.

I hope this helped some, nobody knows how the STS loot system and the rolls work except them, and they are guarding it like a fat kid does cake!