Genghis Khan the thug , killer, murderer was a chinese from the lower grade of chinese who they call them names similar to the chinese gypsies; he wasn’t Turkish (or Turkic for that matter), he was Mongol. Mongol and Turk are two different ethnicities.
However, the empire of Genghis Khan conquered a vast territory in a short period of time. And the land they ruled also included Turkish population in it as well as Arab, Chinese, Greek, Russian, Bulgarian, Persian, Kurdish, Caucasian and so on.
During their conquest, they were ruthless and destroyed many countries including Seljuk Empire and Abbasid Empire.
Because they didn’t have a solid succession system, after the death of Genghis, empire started to divide into smaller countries.
And because, you could rule by shedding blood, only a short period of time (it wouldn’t be sustainable), they started to chance slowly. For example, a Mongol Commander Gulu Khan converted to Islam, after talking with sufi Muslim Haci Bektash Veli. And Seljuk Sultan Alaaddin, settled him and his army which consisted of thousands of men and women in Anatolia. Similar events were took place with the efforts of sufis all around the Muslim territories.
Eventually many Mongol States adopted Islam as their official religion. For Example, Ilkhan Empire, the ones who destroyed the center of Caliphate, Baghdat; converted to Islam. Below, a mosque in Sivas, Turkey from Ilkhan period.
But descandents of Genghis didn’t stay as the ruling class forever, neither they lost their political power suddenly. For example, a Turkish man who lived in Mongol Chagatai Empire married a woman whose grandfather was Genghis. So when he established an empire of his own (Timurid Empire), which consisted of both Turkish and Mongol people, in order to be accepted as the successor of Chatai Empire, he had to emphasize his wife’s relation to Chengis Khan.
However, Babur Shah, the grandson of Timur (and Genghis) who established his empire in India, were regarding his army, his state and himself as Turkish despite his mother being Mongol and having considerable amount of Mongols in his army. He also wrote his memories in Turkish (Not the mention he also mentions a lot about Mongols as different etnicity). That’s why, I think it is wrong to call it Mughal Empire.
As for the other descandants of Genghis. Khanate of Golden Horde further divided to smaller countries. One of them, Crimea became an Ottoman Vassal for centuries. Crimea had both Turkish and Mongol Population and altough, they kept emphasizing their relation to Genghis Khan by using his signature, they kept marrying Turks and adopted Turkish more and more. I don’t think today if there is a single Crimean Tatar who would identify himself anything but Turk. Same can be said about Khanate of Khazan.
Returning to question;
Was Genghis Khan Turkish? Are Turkish people descendants of Genghis Khan?
No, Genghis Khan wasn’t Turkish. And generally, Turkish people are not descendants of Genghis Khan or they don’t have any Mongol blood. But there are many descendants of Genghis who are Turkish.