Is it possible to get a shiny Rotom?

You have to save right next to the Heatran and battle it. If it's not a shiny, then load the game again and battle it. Just repeat this until you...

You cannot catch a wild Rotom in Pokemon Sun or Moon. It must be traded through the Pokemon Bank from another game.

Generally, no. Leather needs to be polished with oils or waxes in order to become shiny. If you want your leather to get shiny, you need to care for it...

Ask a friend with Sun to evolve it for you.

No, the only way of getting the Shiny Charm is by completely filling the Pokédex.

You need to save before talking to the elder or the man that gives you a dratini for 2100 coins so you can soft reset.

Nope. Sorry, but most one-time Pokemon (such as Rotom, Heatran, and the Lake Guardians) will never show back up again if you accidentally knock them out. Newer games do address...

Yes. Until you receive the National Pokedex, you will not be able to encounter Rotom. This holds true for Pearl as well, but not for Platinum, where you can battle...

You could either trade (using the GTS, online connection, or by asking a friend) or use the Pokébank to transfer it from another game.

The easiest shinies to get would be more common Pokémon, such as Zigzagoon or Wingull. As long as you can get a chain going, however, you will be able to...