Wow! Impressive Bob!MovieBob said:Watching Doctor Who as a non-Whovian is a fish-out-of-water kind of experience.
This wouldn't have been the episode I would have suggested starting on, but you seem to have enjoyed it none the less.
On a couple points...
Clara Hate - yeah, I don't get that either. I quite like her. I see in this thread that "inconsistent writing" is one of the reasons for the dislike, but that happens to almost all companions now and again.
Regeneration Haze/Insanity - yeah, that happens in many (although no all) of the changes, and often for the specific purpose of building up the contrast with the previous Doctor. Probably the most extreme examples were the 4th to 5th, which had an entire two hour arc devoted to it, and the 6th to 7th which featured amnesia for an episode. Lately we've seen confusion, but nothing to this degree.
Lesbian Couple - The Silurians (that particular type of lizard people) were an Old Who... I hesitate to call them enemies, since they were usually presented sympathetically. Their plots usually were generally thinly veiled references to Native Americans and colonialism, and often put the Doctor into impossible situations where he tried to keep the peace between two sentient races neither of which he wanted to see get wiped out (generally, the Silurians got the short end of the stick, like the Native Americans that partly inspired them). The Silurians returned in the middle of New Who initially with a very similar plot to their original style, but with the Doctor doing a better job of it this time. Madame Vastra, the Silurian you met this episode, is introduced in a "Dirty Dozen" style team-up of former enemies that the Doctor recruits for a particularly dangerous plan. Strax, the potato-headed guy (a Sontaran medic) was also introduced in that episode and later just started showing up with her. Madame Vastra is actually from Victorian London (where she awoke from hibernation) which is why she keeps returning to that time. Her partner, Jenny, is also a native Victorian. Madame Vastra works for Scotland Yard as a consultant and it is heavily implied that Sir Arthur Conan Doyle took his inspiration from studying her cases (with Jenny as the inspiration for Watson). And yes, the continued appearances of Madame Vastra and Jenny appears to be due almost entirely to their great acting and incredible chemistry.
Strax - The Sontarans were indeed an old Who enemy, but Strax personally wasn't introduced until New Who (specifically in the Dirty Dozen style episode above). I actually suspect that Strax is meant to be a joke in reference to Futurama (and specifically the news-alien). Whatever the truth, he is comedy gold.
Anyway, I hope that answered a few questions and maybe saved you some time looking stuff up. Ta!
Edit:
This mini episode actually does a fantastic job of introducing Madame Vastra.