Pretty much all the show canon species.

For intelligent species mentioned at some point in the pandemic series living somewhere on Equestria's planet (other than the traditional pony tribes) there are zebra, minotaur, changelings, kirin (listed as rare tribe of pony), diamond dog, griffon, dragons, goats, yaks, cow (subsidized into intelligent and unintelligent), buffalo, centaur, and breezies.

Intelligent species that have yet to be mentioned but do exist: abyssians, hippogriffs, kelpies, as well as various unclassified races living under reign of Storm King.

Extinct intelligent species mentioned at some point or another: 'unnamed beholder species', fire lizards, human (different type of human, homo equus are not homo sapiens. Homo equus is an earlier side branch of the human family tree that is not a direct ancestor of homo sapiens, but both share a common ancestor. Homo equus is most closely related to homo erectus or homo habalis, but exact lineage is still debated). There is also mention of other pony tribes that are no longer around.

7584030
And what magic do these species have?

7585779
Which species? There are a lot of species listed. Some don't have strong enough magic to actively ir even passively do anything.

7585999
What magic do you think centaur, abyssinians, zebras, diamond dog, griffin, minotaur, hippogriff, breezies have?

7586122
Most of these are relatively weak in magic. Diamond dogs have magic that helps them burrow and tunnel at much faster rates than should be possible. Griffins, hippogriffs, and breezies all have flight and cloud walking abilities. Breezies also have some limited magic over the wind. Abyssinians, minotaurs, centaurs, and zebras lack any active or significant passive abilities. Still, they can act through potions and artifacts. Hippogriffs are known for using portions if an artifact to switch to an aquatic form. In rare cases, they augment themselves through potions or artifacts to gain active abilities, as was the case of Tirek, who acquired the ability to absorb others' magic and grow both physically stronger and project magic beams.

I didn't do too many changes to Equestria in the Pandemic universe, other than to give some better structure as to how magic worked, since the show was strictly Depending On The Writer. But the species are more or less what they are in the show.

7586336
And what about ordinary animals, they have more intelligence like in the show?

7600833
The spread of magic to normal flora and fauna is a slower process in the Pandemic universe. That's not to say it isn't happening, and there are isolated accounts of both plants and animals showing impact from magic. The most notable example of plants taking on magical properties are the Skytrees grown by Wild Growth. Animals, it is harder to pin down for sure. Arachne's primary pet spider that she spends an inordinate amount of time influencing with her magic is believed to have heightened intelligence, but this unconfirmed how much is the spider and how much it is Arachne directing the spider with her animal influencing abilities. Especially since no real test of the spider's intelligence has been conducted. It is known to regularly escape its cage and return to its cage by its own volition as well demonstrating some limited problem solving ability that hints at higher intelligence than a spider should hace even if not human level. It has also seemed to demonstrate affection and/or possessiveness of its owner.

However, it is believed that eventually, magic will influence the wildlife enough that some species will grow to be more intelligent and possibly reach human-level intelligence. Magic can cause greatly accelerated evolution, as demonstrated by how quickly creatures evolved and diversified in Equestria despite only being a fraction of Earth's age, not to mention the high amount of magic civilizations that developed early in our universe's history. However, even at an accelerated rate, this will take more time than the primary pandemic au stories will cover.

7586771
I don't know if you thought about it when you created this universe, but how many dragon can live in the pandemic universe ?

7791392
Are you referencing Triss's race, which is independent of Equestria's dragons amd are similar just because of convergent evolution? Triss's race except for Triss are extinct. Her race numbered in the billions before going extinct, and had colonized multiple worlds (primarily for resource gathering and waypoints in trade networks). No Equestrian dragons have migrated to Earth. Aside from Spike, the only Equestrian dragon who may have even visited Earth is Ember, for the sake of establishing diplomatic relations.

7793432
something went wrong in the translation, I meant how much such a dragon can live, for example, 1000 years

7793436
Equestrian dragons can live more than a thousand years if nothing kills them first. Most end up dying from accidents, fighting, or disease long before reaching old age, but some do.

Triss's race is not as long lived. While it is hard for them to express age in our terms since they have different concepts of time, we would say a normal dragon of her rave would live a few centuries, with something like 400 or so being considered very old. Triss and Joss are exceptions to this, since they are ascended beings, and effectively immortal.

7793443
and do reindeers exist in this version of equestria and if so, what magic do they have?
https://christmas-specials.fandom.com/wiki/Aurora_(My_Little_Pony)

7797224
Legendary, unconfirmed.

7797260
and what is the attitude of shimmerists to such kirins or other equestrian species ?

7801218
They weren't included by Sunset Shimmer in ETS. So viewed as inferior.

7586771
What kind of magic do you think species other than ponies might possess?

7810389
Kirin have similar spellcasting magic as unicorns, although their spellcasting limits are much lower. However, Kirin are fireproof and do start literally flaming when they get angry, highly agitated, or feel threatened. They also have powerful talents in shaping wood .This is not growing wood, but bending it and reshaping it without breaking the wood. They can also increase other items' heat resistance (although if the new threshold for heat is reached the item will instantly and dramatically burst into flames like the kirin village did when they all went nirik at once).

7810431
do deer exist in the pandemic universe and if so, what magic do they have ?
and what magic do kelpies have?

7810818
I'll leave that one to ASGeek2012 to answer. I can confirm Kirin exist. I don't go much further than that.

7586771
Can you answer the above reader's question?

7793432
and what was the magic of the triss species?

7819555
Triss's species primarily derived most of their magic from the stones of Jeg'galla'gamp'pi. Consider the stone to be like a wizard staff or a unicorn horn for them. The stone had to be atuned to them, and they would have prospective magic users handle thousands of these stones till they found one that reacted with them. Triss's stone was different, it started off as something she carried around with her, but upon ascencion it melded with her. Joss is another exception. He had a stone for some time, but after Triss ascended him he no longer required it.

7819555
Following up on their getting stones from Jeg'gallagamp'pi; even reachng Jeg'galka'gamp'pi took a lot of resources. The planet was precariously close to the star it orbited, and your spacecraft took a lot of resources to not burn up on the trip. Once you got there, there was breathable air and livable temperatures, but there was no soure of food or drink. On top of that, you couldn't harvest stone directly from the planet bevause the planet was all one piece and unbreakabke. You had to wander around and hope to stumble on loose bits of stone.

Faced with these conditions, the hierarchy of Triss's race basically exiled large numbers of the lowest in their society to the planet with the intent of using them to gather the stones. Traders would come seasonally to the planet to trade the basic goods the residents needed to live in exchajge for the stones gathered. Even with the high costs of resources to get to Jeg'galla'gamp'pi, this was a highly profitable venture for the traders. The Hall of the Teachers, the governing body of their empire, would send someone as well to trade for what they arbitrarily decided were the best stones (it was typically just them deciding ehat looked prettiest), as well as gather any of the 'junk peddlers' for training who had stones react to them, they would occassionally bring replacement scavangers if there had been multiple junk peddlers taken over the previous seasons.

It was a highly exploitiyltive economy, and Triss was literally born into it since she was born a junk peddler on Jeg'galla'gamp'pi. She was found to react to what had been consiered the most appealing stone ever found. She was taken, along with Joss (taken to placate her) and their families recieved far higher compensation than usual than the normal season's worth of supplies.

7819564
and how was the magic of homo equus or Neanderthals from a shadow of myself

7820019
The Deneanderthals (characters call them Neanderthals due to their appearance and suspected origin, but they are technically not Neanderthals, but a group descended from that species of human) of Shadow of Myself are non-canon. However, their magic system in that story is still being revealed.

Homo Equus is an extinct species, and there are very little for remains of their species or civilization in the archaeology record, so the mysteries of their magic may remain just that, known only to Luna and Earth's Dreamwardens through their shared memories from the Dreamwarden of that era. With no members of this species still alive, there are no more practitioners of their magic either. There are no known magical artifacts from that era even though the Sunstone is sometimes suspected of being a creation of theirs. The Sunstone actually predates them by eons.