1) “Best Medicine” season-opener, 8 p.m., Fox. If you missed the first season of this charming oddity, here’s the perfect way to meet it. A mermaid (well, sort of) has been rescued (shown here). To help her, townsfolk must admit their own quirks and flaws, which are ample. This hour repeats two days later, when the show takes its regular Tuesday spot.
2) “Marble Hall Murders,” 9 p.m., PBS. So far, it hasn’t been “murders.” There’s only been one linked to Marble Hall (plus one in a related novel). But at the end of this hour, potent events raise the stakes. At its half-way mark, this six-parter keeps building as a terrific mystery.
3) “Trespasses” opener, 10 p.m., PBS. Three great actors propel a moving (and wrenching) four-parter, set in a shattered North Ireland. Lola Petticrew plays a teacher and bartender; Gillian Anderson is her mom, filled with alcohol and despair. Tom Cullen is a crusading lawyer — the opposite of his role in “The Gold,” which takes this time slot next month.
4) “The Terror: Devil in Silver” opener, 9 p.m., AMC, rerunning at 10:08 and 11:16. Here’s another superbly acted (and deeply depressing) tale. After a bad day, a regular guy (Dan Stevens of “Downton Abbey”) finds himself in a mental home where people (including a fragile Judith Light) never leave. The six-parter has lots of high-stakes drama.
5) “Kimora Lee: On Her Own,” 8-9:30 p.m., Lifetime. Lee has always stood out. At 10, she was a big (5-foot-10) Black/Asian kid who was bullied. At 11, she began modeling. At 16, she met her future husband, rap mogul Russell Simmons. She had huge success as a fashion designer and reality-show person, and huge crises; here’s her story.