The problem is that Mary has been--from her introduction on the series--a whining, self-interested brat. That kind of personality does not make others warm up to her, and as I noted above, Luke and Wilder have their own issues to deal with. Mary is supposed to be an adult, yet acts like a middle school teen desperately wanting to be a part of a crowd. One would think that barely-developed medical career would become the driver of her life (remember, she's supposed to be Ms. Mary Do-Gooder of the People, so she should be well-invested in that life), but the "writers" have her moaning about no one giving her the attention she demands (long before the Ivy infection). Poor writing never goes out of fashion on this show, so the heroes are having to deal with a villain who is....needy.
The only way the dysfunctional / split-teams plot works: Montoya and Sophie work against Wilder and Luke, while Discount Joker Marquis somehow discovers Wilder's other life, is protective of her and steps in to deal with Sophie and Montoya. Frankly, at this point, I would be rooting for Discount Joker to be declared the winner, as this Montoya is nothing like the comic or DCAU versions, instead, most of her dialogue is about her obsession with Ivy, and she's a blackmailer who has barely lifted a finger to do her own job---yet now she's become aggressive with costumed people who could turn the screws on her at any time.
As for Sophie, she too has become another Mary--angry because Wilder and Luke will not "let her in" on all Bat-business. Why would they? Sophie is an emotional loose cannon and thanks to burning Virgil's face--psychotic. After the end of the Kate storyline, Sophie has little reason to be on this increasingly overpopulated series.
...because the plot has not said so yet. Luke is the resident genius, so tracking Alice should have been his first thought, but...
Well, what can one expect from a showrunner who consistently prevents the one black male from ever standing up, knowing the weight of his own history and as a result, never taking BS from anyone daring to harm him. Nope, he will continue to be the weak black male who has to lick his neverending series of wounds. If written by actual talents, Luke--discovering any tampering with his suit--would be ready to raise Hell against anyone who threatened his life, but all you're likely to get is the same emotional beats of this episode's conclusion: Luke being apologetic for something he did not do.
Didn't she say she was calling in a favor? If so, that would mean she has some relationship to the person she was going to call, and in Lynn's case, there's no connection at all. Even post CW-Crisis, Luke barely referenced Kate meeting Black Lightning (which was a blink-and-you-missed-it affair) and its doubtful he ever mentioned much of it to Wilder.
Well, Berlanti series can be just as plot/rational character-deprived as so many MCU films, so Wilder being reckless is just part of business as usual.
You've looked at a lot more of this series than I have, but from my limited perspective the storyline with Evil Mary is working right now, as a way for the writers to have her vent her frustrations, which they've been building up in preceding episodes this season.
I do think you hit on some things with Montoya. I like the actress, but her role on the show is strange. She is letting other people do her job, and she is way too obsessed with Poison Ivy. She's really in it just for Ivy, so that doesn't really make her a heroic character. It appears that the Batwoman writers are going for complicated characters this season.
Definitely see what you're saying about Luke, which is unfortunate. You're right about Wilder not having relationships with Dr. Stewart or some of the other characters. Though I would've been fine if there was something that happened off screen to establish connections there with Stewart, STAR Labs, ARGUS, etc. I could imagine Luke more easily having those connections with STAR Labs, and we know he has one with ARGUS through Diggle.