The biggest problem, with the adware, is that I'm using the phone as a security camera using the Alfred app, and once the ad pops up on the phone, the camera shuts off. I can't turn off the wifi, because I need it enabled for Alfred.
I've factory reset the phone, and disabled or uninstalled all the apps I thought looked suspicious, and yet somehow, occasionally, it will reinstall the apps. Every time I clear, uninstall and disable things, I think I've finally got the problem permanently solved, but then out of nowhere the apps are suddenly back. The last time, the phone lasted several weeks before reinstalling the apps. The previous time, it lasted about a day or two.
I believe at least one of the systemapps I disabled somehow reenabled itself, so that may be the culprit. It's called "Wireless Update". There is also a potentially suspicious system app called "Update Service Core", but I can't disable or uninstall that. I've been using "Data usage" to try to see which apps have been active, but it's hard to tell, but it's not clear form the user interface when the activity took place.
Some of the Adware apps are called "Shortcuts" and "Movies-TV". As far as I can tell they're fairly simple apps that use Android System WebView or something similar to display a website, and then popup ads occasionally.
I tried several virus/adware apps and none of them have been able to detect anything.
At some point there was an update from the manufacturer, and afterwards the problem became worse. In hindsight, I should have rejected it. As far as I know, there are no alternative roms, on the internet, for this device.