Thanks @globoy for the quick and detailed response.
I've always seen 0.1uF capacitors on ESP8266 datasheets and schematics, although the reset button has never worked in my past implementations, maybe that's why. That's very good to know.
I added the capacitors to the MCP73871 and the voltage divider to VPCC. I might add the timer too, but I've noticed it is often activated also after times shorter than 4hrs (I suspect this is related to temperature faults). This makes the battery recharge much slower and sometimes the recharge seems to stop forever.
You're right, the USB frame should be just tied to ground, I think I've taken the two resistors from some past projects and, since it was working, I didn't question myself too much.
As for the PSU, my plan is actually to use the most reliable solution that allows my board to live the longest, that's why I opted for the TPS63051 buck-boost. Making the battery last longer is secondary, although I'd like to achieve a duration of 24hrs by using a 1200/1500mAh LiPo.
I use both 12k and 10k resistors multiple times in the circuit, so I don't think I would save a part number anyway, as some 12k resistors are also suggested by the datasheets themself. Unless I replaced all the 12k with 10k, also for the nCTS and nDTR?
I selected those voltage divider resistors cause I needed to optimize the signal resolution by only considering a smaller part of the full range. In my application, the sensor never acquires a value above 50% of its full range, so I don't think there will be any risk. However, I'll double-check this too, just in case.