Absolutely agree with Archie jon. Thought something like that ages back. You could have companions from different time periods (at least the ones still alive, or from the modern series), maybe an episode a week covering a different period each; one set in modern day UNIT following Kate Stewart, one of say Benton remembering back old UNIT days, one of the Paternoster Gang, one of Captain Jack buzzing around space, Nyssa working aboard the Terminus looking for a cure, one set on Gallifrey following Leela or Romana during the late days before the Time War, Mickey and Martha's independent alien-busting days, Rory and Amy's 1930s life etc. etc. Could either be one-offs, or have some overarching arc containing a theme or something, or a shared threat over time and space or something. Basically rip off the companion chronicles and put it on TV (ha ha). But yeh I like the title of The Worlds of Doctor Who or something. Could be a interesting way of showing the Doctor's world from a sideways angle and what it looks like, or what the effect of the doctor being around especially when he/she has vamoosed. The beauties it creates, and horrors. The effects it has on people, for good and better.
Yes. I found her insufferably annoying, and frankly she only seemed to be a woman to be used as a gag, rather than having any genuine purpose (much like Jenny and Vrax "lolz they're lesbians aren't they!"). If they do have to bring him/her back (and really they could wait a while if they wanted) I agree with your suggestion of a more Delgado-esque one, although preferably I'd like him to be played like Gus Fring in Breaking Bad (lethally efficient, utterly dead-faced and unemotional, suppressing a deep layer of murderous rage - it'd be terrifying). Although it depends on what Jodie Whittaker's doctor is like in order to play off, as they have to be mirrors of each other really to work best.
Alan Turing. Think you could do a really tragic and beautiful episode about it, although you'd basically just need to do 2014's Intimidation Game with the Doctor in it (and an alien), so it won't be probably done soon or really be needed right now.
Time Flight was truly one of the worst things I think I've ever seen. Black Orchid is dull beyond comprehension. Most of Season 7 of new who. Probs more but I can't remember.