There is some information about this on the Systematics page, so I'll try to summarize.

Scrolls are a special kind of items. They can be equipped on your characters, giving you one extra action (skill) while equipped. Think of them as FFVII's materia, with the difference of being all of them unique. You can't buy neither synthesize scrolls, and there's only one of each in the entire game (a total of 27).
As for what scrolls can you encounter...

One support and one offensive for each element (8 elements: Fire, Ice, Thunder, Water, Earth, Wind, Light, Gloom). 4 physical skills. And 7 uncategorized.

I'll leave them as a surprise for now. I've tried to make them as diverse as possible, and to use the most of the mechanics I've been adding.

Fylgjas on the other hand are guardian creatures that you equip to your characters. While equipped, they raise your stats depending on that creature's level, and give you two extra battle actions (again, skills). Very much like FFVI's espers. But you see, they have a level attribute! Fylgjas can level up very much as a regular character, unlike espers which gave a permanent boost to the character that has them equipped. This is mostly to give you the chance of swapping characters and not having to raise all of them.

There's also another important thing to say about Fylgjas. And that is, summoning. When in battle, you can use the "Summon: Name" command, making the fylgja emerge from your character and fight side-by-side with you. Thing is, they are not entirely corporeal, more like a phantom, so they don't die, unless their host dies. Bad thing is that you lose temporarily their bonuses when in this state, but the Fylgja get to fight using their own pattern, which is also influenced by the Fylgja's level.

There is a limit for summoning, thought, and that is only one "active Fylgja". If you summon another one, the previous is automatically unsummoned.

So, the characters slots look like this (as you probably seen in the screenshots section):

Character status screen

• Scroll 1
• Scroll 2
  
• Fylgja

Character equipment screen

• Right hand
• Left hand
  
• Head
  
• Body
  
• Accesory

The other equip slots are pretty much vanilla. Only difference with RMXP's vanilla equips is that some characters can dual-wield (which is a feature not missing at any other RM version).

Moving on to the last issue, is the weathers. Everyone knows that RPG Maker has a nice "weather system", but it's just graphical. So, what did I do? Pokémon weather.

Normal: Ups fire elemental damage, lowers water elemental damage.
Rain: Ups water and thunder elemental damage*, lowers fire elemental damage.
Thunderstorm: Ups water and thunder elemental damage*, lowers fire elemental damage.
Snow: Ups ice elemental damage. Small chance of Hypothermia** status to all battlers.
Sandstorm: Ups earth elemental damage. Deals damage each turn**.
Hurricane: Ups wind elemental damage.
Fog: Reduces all battler's base accuracy to 80%***.

* Rain raises a lot Water damage, Thunderstorm raises a lot Thunder damage.
** Snow and sandstorm side effects depend on each battler weaknesses to their respective elements (ice and earth). Sandstorm is one that can actually recover your earth-absorbing allies.
***There is a buff to make anyone NEVER miss (Unblockable), so don't be scared.

And that's it for today, thanks for reading,
Orochii Zouveleki