was any music video shot for the first song?
Yes
What Have You Done for Me Lately
The accompanying music video for "What Have You Done for Me Lately" was directed by Brian Jones and Piers Ashworth and filmed in December 1985. 
what is control? A third studio album whose album? American recording artist Janet Jackson when was it released? February 4, 1986 can you name a song from the album? "What Have You Done for Me Lately", "Nasty", "Control" where was the second song performed live? At the 1987 Grammy Awards, at the Aloha Stadium in Hawaii, at Essence Music Festival in New Orleans is the above artist the composer of this song? Yes
wiki:12538850
What Have You Done for Me Lately [SEP] Music video
The accompanying music video for "What Have You Done for Me Lately" was directed by Brian Jones and Piers Ashworth and filmed in December 1985. The video's choreographer was Paula Abdul, who appears in the video as Jackson's friend. According to a "Jet" magazine publication in 1990, in the video Abdul "combined sexual energy with classy, alluring moves. The combination propelled Janet into the classification of sexy superstar. Any who saw the videos witnessed the fact that Janet was, indeed, a full-grown woman." The video also featured Tina Landon who would later become Jackson's choreographer. Jackson shared in her book "True You" in 2011 that her recording company thought it was important that she appeared thinner in the video: "I'd been told that my whole life, but at this critical juncture, with my career taking off, I didn't have the wherewithal to argue.