Hello, I was wondering if there are any Manga that revolves around the MC going on Undercover Time travel missions to help solve a mystery or save someone from their demise or prevent a terrible event from happening?

Boku Dake ga Inai Machi is a well known one. I only saw the anime & didn't read the manga, but it was very good. It's a pretty common trope so you might want to try an advanced search with the different tags that start with "Time" (look at Boku Dake's tags).

Uuhh...
Orange (TAKANO Ichigo) kinda? The characters themselves don't travel, but notes/things from the future get sent to the past so

...if you're fine with manhua "A Journey to The Past" (寻找前世之旅)

Not sure about undercover part but
Time Patrol bon