>>/10206/
> The only reason I can think of for why Celestia would be surprised by this would be that Twilight only sends her letters on certain days. 

> letter-writing portion at the end of an episode falls on a Saturday in-universe. 

> It would mean Twilight’s been in Ponyville for 5-6 weeks, which feels right 

I am not sure I agree with episode air dates equaling dates of the episode, but I do like the idea of the time frame and that is a interesting detail with Celestia.

> It makes it clear in both episodes that she’s taking her studies seriously, but hasn’t quite found her footing yet. 

Twilight Sparkle here feels very fresh out of her time at Canterlot avoiding social interactions here. She isn't acting anti-social but she feels more cold and distant. 

> followed by this chemical experiment she’s doing. Is it somehow related to her friendship studies? Who knows, I’m probably going to keep pondering it though.

On the chemical experiments, Twilight was the smart character and thus, at least in the early 3 or 4 seasons, she sometimes being studying random science stuff just because smart character trope. I don't mean this as a wholly out of universes explanation either. I think she has some side pursuits and such chemical experiment might be unrelated!   

 >>/10207/ 
>  but there’s just no way for an adult to watch this episode and see Dash and Gilda’s friendship as platonic, I reckon – at the very least it’s an angle I can’t imagine the creators being unaware of, even if it was accidental or unintended in some way. 

If it had been a couple seasons in, I'd might agree with you, but here, I am not sure if that would've been an intent at all. I don't feel a romantic energy so much as old high school best friend and Rainbow Dash discarded her rather quickly.  There is a longer point I want to make and I do want to examine this further but my brain is a bit tired to make it right now. 

> Also it occurs to me that Gilda’s confrontation with Fluttershy was kind of set up earlier in the episode where Pinkie says that Fluttershy’s too sensitive for pranking.

That is good writing there.

> If I were cynical I’d even say she might have suggested the idea to Dash, but who knows, Pinkie’s mind works in mysterious ways. 

I completely agree that the party was weird and that Gilda was right to feel targeted unfaily even if she is a jerk. As for Pinkie Pie, she and Dash aren't mean spirited enough for me to go the full cynical route either but the tone is still a bit odd. 

> The religious significance of the Princess in Equestrian society is overblown in the fandom, but it is based on existing themes within the show, and it makes me wonder if under Twilight’s reign as Princess

Especially at this time, when the assumption was that they were a goddess (well in fairness,Celestia's  name is used in that manner). Raincheck on Twilight roll and potential religious aspects to her roll.