I just have a couple more questions. The first one is about stars with enemy sylesties. I've seen a couple threads but they haven't answered all my questions. What is the difference between two white stars and two green stars? Do the color of the stars mean anything? Why are three white stars common and two green stars uncommon? The other question is about festivals. How often do they happen? Are they the same ones each year? That's all for now, thanks.

Color of stars = rarity
Number of stars = difficulty

Link: https://www.sylestia.com/forums/?thread=13&page=72#718 Author: Flute Time Posted: 6/26/2016 at 5:42 PM It's the genes, specifically the genotype points. (for the table below, just look at the new system, looks like the old system is starting to match) Colors are randomized.

As for the festivals, they're almost always annual (I can't think of any that only happened once). They often happen per their season or holiday.
To give you a basic idea, the names of some of the festivals (and I'll name in chronological order as I remember them, starting from January) are:

Winter Festival
Week of Love (for Valentine's Day in Feb)
Week of Luck/Fortune (for St. Patrick's Day in March)
Spring Festival (may overlap with Easter)
Summer Festival (may overlap with 4th of July, American holiday)
Fall Festival (usually has Halloween)
Thanksgiving/Black Friday
Winter Festival again

They repeat each year, and most of their features stay the same (Winter fest has advent calendar and baking, Spring fest has gardening and egg hunt, Summer might have treasure hunt again, Black Friday might sell old monthly items, etc), with some new content (usually new avatar items, new themed pets, etc).

Hope that helps!

Further, the number of stars represents the Mana a pet will have if caught (not just the difficulty of the fight), and is unrelated to the GP that the colour represents.
Bosses (five stars) cannot be caught, but other than that:
* = 60 (example)
** = 80 (example)
*** = 100 (example)
**** = 120 (pretty rare to come across, so we haven't managed to catch any)
(Fabled pets have naturally higher base stats; ** = 100, *** = 120, **** = 120. 120 is the maximum possible mana)