I have some skills published for Alexa, so here my understanding...

When you use Alexa, it needs to connect to the cloud, where you send whatever you say as a digital signal. How long Amazon will keep this recordings?, good question, not long I guess, they might keep the text?...

"As far as I can tell, most data from the Amazon Echo (e.g. recordings of my commands) are stored in the cloud, according to the Alexa FAQ. However, I couldn't find any authoritative information about what information is stored on the device itself."

Now the device itself is not powerfull enough to store much, may be the Echo or Echo dot, could have some memory but I will think is more to handle internal processes, not so much to record you?

If I ever wanted to sell the Echo, it'd be useful to know what information is on the device, so that I can try to remove it.

you can unlink the hardware from your amazon account, so the info might be kept by Amazon, but not on the echo

What personal information is stored on the device itself? Amazon login credentials? Cached data from skills?"

As commented before, the real data is on the cloud, linked to the Amazon account associated to that echo.

But good question, it could record some things? A teardown shows storage... 4GB Toshiba eMMC NAND flash So yes, it could store something?

Personal information stored?, maybe...

Now, to hack it on the hardware, retrieve what is in there. Your concern?... Might be more difficult?, there are easier ways to record that audio?.

For a hack in AWS, alexa, could happen also, but more difficult?. Your info for sure is collected not only by Amazon, but many others like mobile operators, advertisers, mail providers?...