#1 the Audiophile 2496 RCA input is for LINE level....not mic level. Plugging a microphone into it will give you a crappy low level signal.
#2 TRS and TS are just connectors. They are used for specific purposes. TRS can mean a balanced connector...but not always. You can use TRS connectors in a non-balanced path. The connector only helps carry signal down the cable. What really matters is the start and end of the gear you are plugging into. If the gear you are using has balanced connections, you use a TRS cable where tip is hot and ring is cold. If it's a stereo connection, you'd also typically use a TRS connector. It's not the cable that makes the signal balanced or stereo, it's the gear.
you need to plug your SM58 microphone into a microphone preamp. And then run that preamp into a line level source (like the 2496 RCA inputs). RCA is an unbalanced connection, so TS->RCA adapters are fine. TRS->RCA will work also, it just won't remain balanced.