she was probably barefoot because of her swollen ankle, it was probably easier than just walking with one shoe in one foot
Any person could've called the paramedics, whether it was set up or not, it's not unheard of that places like hotels and restaurants have whistleblowers, or people tipping the paparazzi especially when they know celebrities frequent those places. Maybe it was the hotel's staff since they can't risk having an injury or accident in their premise and not doing nothing.
Who knows if Britney was forced to cooperate with them so they could verify she was alright, that's why they were outside. If they left without her, it's because they didn't think it was required, or Britney was conscious enough to refuse their service.
In the video we can see her assistant was there trying to cover the paparazzi's camera, and then we see someone arriving in a car, which seems to be Cade (he's driving a Tesla, does anyone know if he owns a Tesla). Anyone could've called Lynne as well, who knows.
The pictures may "speak volumes" but then you see the video, and there doesn't seem to be nothing bad happening at all.
If this happened at midnight while she was partying, when she hurt her ankle it must've been very painful, in the middle of the commotion I doubt anyone would be calm enough to go and put on some presentable clothes for the press that might be waiting for her outside (which shouldn't have been). Yet they were thoughtful enough to give her a blanket and the pillow to cover herself. She probably just wanted to get out of there asap. We don't even know if she was topless, probably she was wearing a bra/bikini.