Regarding theme questions: Wilbur Hatch, head musician for CBS, composed and conducted Suspense music. As Twilight Zone was a CBS program, music could be recycled. As half of the Alfred Hitchcock Presents seasons were by CBS, some music might even pop up there. (BTW, he was also known for music on CBS TV I Love Lucy.)
I need to go through all the CBS Radio Mystery Theatre episodes again to verify, but I'm pretty sure I remember Hatch credited for music there. Wikipedia says he died in 1969, but perhaps even afterward they used his music. (As side note, Lorene Tuttle and Agnes Moorehead, popular in Suspense, often appeared in CBSRMT.)
Growing up in 1970s radio stations always played OTR reruns. At 10 I heard the first CBSRMT episode as it aired. So I got some inkling of what the Golden Age of Radio must have been like. (To know what we're really missing, one has to listen to WJSV's Complete Broadcast Day from 1939, also found at Internet Archive.)
There *are* new radio shows being produced. Seattle's radio station KIXI also streams online, hosting contemporary radio shows including Twilight Zone radio series and Imagination Theatre. (In addition to the infamous :-P Radio Spirits show When Radio Was.)
Personally, I still prefer old radio, TV and movies from back in days when people spoke at a slower rate, reflecting simpler times--and adding to any suspense.