There is no ADC (analog) peripheral accessible by the LP-core on a ESP32-C6.

I've forgotten to put paste under the ground pad entirely before. That is probably a bit more obvious than a couple missed pins :) So, the problem solved after putting paste properly? The ground pad is underneath on a module. The fix is to desolder the module and reset it with the proper paste.

The most likely cause of this is a bad USB cable/port. Try a different port with the highest quality cable you have.
That said, applying 9V may very well have damaged the flash without injuring the cpu. This could appear to the esp32 like a communication failure.

There are 4 independent PCNT units on an esp32-s3. There is not an arduino wrapper for pcnt, but the IDF functions will work if you just include the appropriate headers.
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The ESP-IDF example should essentially work. Use steps 1-3 from the example, then call LittleFS.begin with the partition name you gave to the external flash. You won't be able to do standard OTA on that space, but with some creativity you could load firmware from it.

I'm pretty sure this would not be possible in arduino, since any extra RTC_FAST memory is going to be mapped into the general heap. It might be possible to do in an IDF project where you separate the RTC memory, but I am doubtful that the ULP would be able to pick up a dynamic resizing by the cpu.

I assume this is the sort of mini device that only has a direct USB connection. In addition to the boot button as suggested above, you will want the following settings in Arduino IDE. Note that I consider these devices very poor for developing code, since it takes ~200ms for the USB CDC connection t...

I don't have a good answer for you, other than you are asking the system to do too much. Here's a couple recommendations 1) I doubt you really need the data every 100ms. Collect 10 data points and send them in a single packet. This is a lot less network overhead, and easier to sequence. 2) Bluetooth...

Those pins are for extra data lanes that would be used in Quad SPI . QSPI is not currently supported in arduino, so can only be enable using the ESP-IDF drivers. If you aren't using those pins for QSPI, you should be able to use them for whatever you would like. Perhaps your board is using gpio 14 f...

Without actual code demonstrating the issue, nobody is going to be able to help you. This is very likely a priority issue. Loop task runs at priority 1. Start a new task at priority 6 and put the led flash in that.