Here we go!
1. The songs were:
My Dad and She Can't Find Her Keys, performed by Paul Peterson in the role of Jeff Stone.
Johnny Angel, performed by Shelley Fabares in the role of daughter, Mary Stone.
2. The Beverly Hillbillies. The song was written by bluegrass performers, Flatt and Scruggs, who also made several guest appearances on the show.
3. In the 1960's, he wrote the theme song for the very popular show, Peter Gunn. In the next decade, the 1970's, he took on another form of detective show, the theme from Charlie's Angels.
4. The group was The Doors and the song was their mega-hit, Light My Fire. Mr Sullivan objected to their using the word "higher" in the lyrics. Although they agreed to change it, during the live telecast they left it in. This infuriated the powerful Mr Sullivan and he refused to ever have them on his show again.