This post refutes the claim that researchers found a "backdoor" in ESP32 Bluetooth chips. What the researchers highlight (vendor-specific HCI commands to read & write controller memory) is a common design pattern found in other Bluetooth chips from other vendors as well, such as Broadcom, Cypress, and Texas Instruments. Vendor-specific commands in Bluetooth effectively constitute a "private API", and a company's choice to not publicly document their private API does not constitute a "backdoor".
It is not. ESP32 is an embedded chip with less than one megabyte of RAM. It cannot run apps or load websites with any malicious code, it only runs the firmware that you flash on it, nothing else, and of course your firmware has full access to every chip feature. If your firmware has a security hole, it’s not the chip’s fault.
Try reading the article next time.
There was no mention of over-the-air exploit, so eh.