Hi! Welcome to Sylestia. I outlined the answers to your questions below. c: Included a bit of extra information too. ^-^

AP (Advancement Points)

AP stands for advancement points. You can earn AP by battling enemies that are around your user level. Your user level is found on your profile page. (Currently your user level is 19). Your user level is based on the highest leveled pet that you have personally leveled up.

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Number of Pets in Party

As you advance through the storyline you will unlock pet slots. In esior's haven, if you go to the plaza, and scroll down to the trainer, there should be a button to increase the number of pets in your party.



I believe when you get to the second area, in the plaza you can again increase the size of your party. I think the first increase costs 10k gold and the second increase costs 25k gold.

Currently the maximum number of pets in a party is 3. And the level cap of pets is 60.

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Rarity: Armor

There is a rarity system for armor.



Green is the most common. Then blue (rare), then purple (epic), then orange (legendary), then red (mythical). For armor, the price value does indeed correspond to their rarity. The only other thing affecting armor price, is the armor level. You could have mythical armor for a level 5 pet, but it will not actually be worth much since level 5 pets can't do anything.

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Rarity: Items

The same rarity system is also used for items. except there are no red (mythical) items.



While this rarity system is in place for items, it does not necessarily reflect an item's value. The other factor is how it was obtained and when it was obtained. An item gotten 2 years ago that has not been re-released is generally worth more than an item that is available today. i.e. older items are generally more valuable. The items that are harder to get are also worth more. Lastly, items that are more popular are also worth more as well, but this isn't too big of a factor in the scope of things.

For perspective on what items cost, I would look at the Trade broker.

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Rarity: Tamed Pets

There is a rarity system for wild (enemy) sylestis. It uses the same color system: green, blue, purple, orange, red. Green wild pets will have 1 gene point of traits (i.e. 1 carried trait -- not visible), Blue wild pets will have 2 gene points of traits, etc.



Note that the number of stars just indicates how strong that enemy is for its level. Has nothing to do with rarity. Generally capturing tamed pets is for personal satisfaction. Regular tamed pets aren't actually worth any gold at all unless then are of orange star or better. The only exception is tagged pets (also synonymous with themed pet). You can check whether a pet is tagged/themed or not in the genetics section at the bottom of the pet's profile page.



When finding a tagged pet in the wild, it will be named e.g. instead of being called "Wild Zolnixi" it will say "Hot Chocolate Zolnixi." In the festival zone log it will state that you've encountered a rare enemy when you have found a themed pet. Note that tagged/themed pets can only be found during a festival.


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Rarity: Price of pets in general

Once you've caught a pet or bred a pet, etc. there isn't much in place to denote rarity. But here is how they are roughly priced.

Tagged:
Sylestis that are tagged/themed are expensive. Where Fabled tagged pets are the most expensive. Fabled pets are one of the following: Nephini, Aeridini, Puffadore, Griffi, Ny'vene. They are fabled as they are not found in the wild other than in a festival zone. Generally the price of fabled themed pets ranges from 500k gold to 5k (5,000) diamonds.

You can search for pets that are up for sale through the advanced search.

Purebred:
As you know, there is also breeding on Sylestia. Purebred pets are pets that have been bred from solely themed pets and their offspring. They can be worth from roughly 25k to 300k gold. This is an example of a purebred pet. If you click the lineage button in its profile page, you'll get to this page. A pet with a star means that it is a tagged pet. You can trace a pet's lineage to see if it is purebred or not.

Stat Pets:
Through breeding one can increase the base stats of a pet. If you look at the statistics section of this pet then you will notice it is level 0 but has Strength, Intelligence, etc. all at 100. It's easier to battle with these pets than regular pets. Think super buff pets. xD These pets range from roughly 200k gold to 500 diamonds, depending on the seller.

Regular Project Pets:
Sometimes people have a beautiful pet in mind. So they through essence or dye try to work towards their dream pet. And then sell offspring of the dream pet that they have achieved. These offspring generally range from 25k gold to 200k gold.

Regular Random Pets:
Anything that isn't in another category falls here. Pets bred randomly. Pets with no visible traits. Etc. These pets are generally worth from 0 gold to 25k gold. The majority being worth 0 gold.

Conclusion:
While there is a market for all of these special pets, their price reflects the means to create them. Generally one spends more obtaining these pets than their sale price. Pets are more for personal satisfaction.

Fun little thing I learned that I wanted to share:

Do you know about the strength stars that enemies display? They show up in the top-right corner of the enemiy's info and tell you how strong the enemy is. For most enemies, these will range from 1 to 3 stars with 1 being weak, 2 being normal, and 3 being strong.

On to my point. I bring up these stars because they don't just tell you how strong an enemy is, they also determine how many APs you will get for defeating that enemy.

So if you encounter a battle with 3 enemies and they all have 1 star, you should get 3 AP when you win. You'd also get 3 AP for winning a fight with a single enemy that shows 3 stars.

EDIT: Found the limit to be 25 levels. Discovered this while doing daily quests and found that when an enemy was 25 levels or more below my pets, that I no longer received APs from them.

I also found that the stars determine how much reputation you gain for the town of that area, but this doesn't appear to have a cut-off.