Question: Are there any legends and myths on the Alihah? I'm really interested in delving into them.
Extremely few, actually, but in our opinion that's all the more reason to delve as much as possible.
The pre-Islamic religion of ancient Arabia is one of the most poorly preserved in the world. The people who practiced it were largely pre-written-word, so they didn't leave us any convenient texts about their beliefs, and furthermore they were heavily invested in worship centered around natural features of the world, especially stones and groves of trees, which means they also didn't build very many religious structures that we can investigate for archaeological clues. Of course, we've worked with less than that before, but the final nail in the coffin was the sudden and overpoweringly influential rise of Islam in the region at the beginning of the seventh century. Muhammad's crusade for his god was devastatingly effective at destroying every trace of the area's previous beliefs in order to better serve the glory of Allah, which means that what religious artifacts did exist were mostly smashed, burned, or taken by Muslim conquerors to become part of their own new religion.
With all this going on historically, it would be hard enough to find out anything concrete about the ancient Arab religions, but thanks to the area remaining strongly Muslim through the intervening centuries, there also hasn't been much of a concerted effort to investigate the ancient religion, either. The first few centuries of Islamic rule involved systematic destruction or assimilation of anything that came to light after having survived the initial pillaging, and while we have a few records by Muslim scholars of the time - The Book of Idols is the most famous and useful for the study of the Arab gods - they're not numerous and very obviously biased in favor of Islam. Muslim scientists, historians and poets went about spending a few hundred years studiously ignoring the unworthy older religion while making leaps and bounds in the study of other kinds of in history and culture, and the result is that today there's not even all that much interest in the subject, let alone active work being done on it.
Of course, there are intrepid Muslim researchers out there right now trying to preserve and discover more about the ancient religion of their forbears, so don't think there aren't. But compared to the renaissance of study that the European and Egyptian religions underwent during the nineteenth century, the field is almost deserted. And what folklore does remain is usually not translated into English, because if there isn't much interest in the subject in Saudi Arabia, imagine how much less there is in Europe and the Americas, where the average person on the street probably doesn't even know that there was a pantheon that predated Islam.
However, there are a few Arab myths still floating around, and I am here to share them with you! Since they were almost all recorded by Muslim writers, you get the same kind of monotheism-triumphing-over-the-dark-ages stuff you get with Christianity in Europe, but filtered is better than nothing.
The story of al-Uzza is probably the most famous, although also the most tragic (and obviously affected by Islamic influence). The great goddess al-Uzza was the patron of the Quraysh group of Arabs, which was also the people of Muhammad, who in his youth sacrificed goats to her. When Islam became powerful in the region, even including verses against al-Uzza in the Quran, the Quraysh were dismayed by the opposition to their deity but remained steadfastly loyal. When abu-Uhayhah, ruler of the Quraysh, became fatally ill, he spoke to his successor abu-Lahab, saying that he was afraid that after his death al-Uzza's worship would cease. abu-Lahab assured him that al-Uzza's worship had been strong before his birth and would remain so after his death. Upon hearing of this, however, Muhammad called upon Khalid, one of the greatest Muslim heroes of the time, and ordered him to go to al-Uzza's sacred grove to root out the religion. Khalid complied and went to the grove to chop down one of its trees, thus hoping to render the goddess' worship powerless, but upon returning to Muhammad was told that this was not enough. He returned to the sacred grove again and chopped down another tree, but again was told that his efforts were insufficient. Finally, he returned a third time and cut down every tree in the grove, at which point al-Uzza herself appeared, looking haggard and miserable and wailing and gnashing her teeth. Khalid then killed her by slicing her head in half as well as murdering her priest who tended the grove, and declared that Islam had triumphed over the pagan creatures. The myth is pretty clearly not one written by those Arabs who were fans of al-Uzza and would never have dreamed a mortal could hurt her, but that's monotheistic revisionism for you.
The short story of Isaf and Nailah is also partially preserved by Muslim writers, although most likely in a radically altered form. In the Islamic version, Isaf and Nailah were an insufficiently pious couple on their way to Mecca, and upon arriving there at the end of their pilgrimage, they had sex inside the Kaaba, which so infuriated Allah that he instantly turned them to stone as a warning to all others. However, evidence suggests that Isaf and Nailah were probably originally pre-Islamic deities and that this story was invented to de-divinize them and make them figures of ridicule who reinforced Allah's position as the most important god in the area. The stones that were once the two lovers are theorized to have represented guardian gods who protected pilgrims on their annual hajj for religious destinations or festivals.
Another myth is a future prophecy, something predicated by the prophets of Islam but not yet come to pass, which concerns the god Dhu Khalasa, a deity of justice and redemption. The god was reportedly worshiped by ecstatic rituals including dancing and veneration of his shining white nisab, which was housed in the Kaaba of the South, a major hajj destination; although the second Kaaba was destroyed on Muhammad's orders to prevent it from being a rallying point for the older religion to compete with Islam, it is predicted that one of the signs of the end of the world is that the women of Dhu Khalasa will once again dance (the exact wording is closer to "a commotion of their backsides", so you can enjoy this example of an ancient prophecy that predicts booty-shaking) around his nisab. Whether this means a literal end of the world or just the end of Islam's world and return of the ancient beliefs is up for debate. Interestingly, it might be argued that this already did happen; despite the destruction of the southern Kaaba, the worship of Dhu Khalasa resurfaced later and was only finally destroyed as recently as 1815, when more modern Islamic groups stormed the reconstructed temple and demolished it and its nisab with gunfire. Of course, the world is still here and so is Islam, so if that was the fulfilment of the prophecy, what did it end? And if it wasn't, why not and when will it actually be?
Finally, there's the story of Iram or Ubar, colloquially called "Atlantis of the Sands", a lost city of an ancient Arab tribe said to be buried somewhere in the desert. According to Islamic myth, King Shaddad of Iram conquered and united all the Arab peoples and some of the nearby Canaanites as well, creating a giant kingdom that he ruled from his capital city, but the people were worshipers of the ancient gods and therefore drew the wrath of Islam. The famous Muslim prophet Hud went to the city and demanded to the king that they convert, but Shaddad refused. Allah retaliated by causing a massive drought, but when even that could not force the people of Iram to abandon their gods, he finally destroyed the city with a massive windstorm, which smote the city so violently that the entire place sank into the desert and was swallowed up, leaving behind only a few faithful Muslims who had been living there.
As the above stories pretty clearly show, the vast majority of Arab mythology we have remaining is embedded in Islamic mythology, from which it has to be isolated and interpreted without any guarantee that what stories remain aren't heavily rewritten by the rival religion over the many centuries between then and now. Most of these stories were created by Muslims who wanted to illustrate how much better their god and religion were and how thoroughly they triumphed over the pagans of yore, but even so we can find a few kernels of truly ancient belief within them. And modern Islam itself still contains a great number of religious concepts and practices, including the hajj, circumambulation of sacred sites, and even the Black Stone of the Kaaba itself, that are probably at least partially based on ancient Arab practices.
So there's no Bhagavad Gita or Theogony for the ancient Arabs, no coherent ancient body of myths or running narrative of stories, but we do still know a thing or two about their gods and what those gods did for their people. The unique desert-nomad culture the gods were based in and the subsequent almost total wiping of all evidence of their existence makes them a fascinating pantheon to study and theorize about, even if most of our information comes from archaeological evidence and descriptions of worship rather than easily-told stories.