1. There's a whole bunch of tips people could give you, but to keep it short, talk to everyone to try to get as much free stuff as possible, use Pokemon and strategies you might normally would, and (optionally) use multiple Pokemon on your team in rotation depending on which are better for a certain fight. Also make sure to look at what each Field does, since they're used in some battles: http://www.pokemonreborn.com/game/fields.html
2. You can only steal them from wild Pokemon using Thief or Covet (as long as the Pokemon that is stealing the Item doesn't have an Item). To improve the chances of wild Pokemon having an item, you should use a fainted Pokemon with Compound Eyes in the front of your team.
3. Exp. Share is available from a side quest, Leftovers is from Pickup.
4. There's an obtainable Pokemon list: http://www.pokemonreborn.com/game/obtainable.html
And a Pokemon Location list: http://www.pokemonreborn.com/forum/index.php?showtopic=16407
5. Move Relearner Key isn't available until you get your fifth Badge. It will be in the Underground Railnet train track puzzle (available only with Strength). There are cracks in the wall you can Rock Smash, one will have the Key. She is useful for some Pokemon like Gallade, which gets a lot of coverage moves from it.
6. Heart Scales and Shards are used to buy things. Heart Scales are used for the Move Relearner and Nature Changer, while Shards can be used for Tutor moves, puzzles, Ability Capsules, some Pokemon, etc. The Shards are usually used in 7th Street and Agate Circus, which are much later in game.
7. I'd just use Bulbapedia to see what those Items did. The Iron Ball cuts your Pokemon's speed in half, though.
8. Training items for EV Training definitely helps, but isn't necessary for beating fights.
9. I haven't really used Shinx, so I can't help you that much. It has good stats, and Guts could be nice to work with, but it doesn't get many good moves... I prefer using Ampharos, which is free and only a bit after Shinx.
If you have more questions, you can post in this thread: http://www.pokemonreborn.com/forum/index.php?showtopic=3876
Hope you enjoy playing Reborn! :]