I've notice it's dificult to say the rarity of a pet with no reference, for example: I caught a rare Vulnyx that aparently has only one showing gene and without something saying that she's a rare pet, it's hard to see or prove it.

Maybe I'm not the only one with this problem, so it'd be nice if there is something - like an inscription in the profile page - that can proof the rarity of a sylesti. Thank you!

I agree with this idea, and add to it the thought of marking event pets as such. Like letting people know that the chocolate bulbori from valentines day is a legit g1 pet and not an offspring or false made one.

There are ways to tell this. Any caught event pet, even if they don't maintain the "special event name" will always say "This is a Captured Sylesti." (You will also find tons of similarly styled Sylesti around the site owned by all the people who participated. I also believe there is a guide somewhere showing all of the special pets introduced to date.) If it doesn't say it's captured, then it's not a legit g1 pet. Instead it would have a "Mother:" and "Father" section linking to the parents of said pet. And if it's a player attempting to clone the general look of event pets then the profile will state that the Sylesti was either a regular or enhanced generated pet where otherwise it would have stated it was captured (depending on if the player used a regular or enhanced essence to try and recreate the look).

As for rarity, those can also be determined based on the genes of the pet, if they have any. The formula basically looks like this:
Common - may carry a trait (or have nothing at all)
Uncommon - 1 visible trait
Rare - 1 visible trait and 1 carried trait
Epic - 2 visible traits

If the captured Sylesti you are looking at has nothing at all, it was a common Sylesti. Granted, you can only tell all this information if you have a testing kit (unless the trait is visible); however, if you're facing them in battle then you should have an idea of what's going on. In the instance of rares, you won't know WHAT the carried trait is until you have it tested (either via a kit or a scanner), but they will always have something hiding under the surface that you just can't see.

all that is right and it's easy to know it, but with the time, someone just can't remember the rarety of each own sylesti, well at least that's my idea... a little reminder always is helpful

Then a quick peek at the profile page should be helpful to remembering. If all else fails, check to see if a Genetic Mutator was used (in which case you know for a fact the pet was captured as GMs cannot be used on generated or bred Sylesti) and, while it may not show which exact trait was added after capture, you can still find out how many it had before the potion was used (just subtract 1).