These are my first two mobile devices as I have always been against them.

I bought them because I need a mobile device that runs apps in order to do many things for work. I can't avoid it.

However, coming from a Linux background, although they are useful devices, they are out of my control.

Although I have avast antivirus installed, programs seem to have the ability to install themselves without my permission. Also, sometimes when I wake up the device, programs are open that I did not open. For example web browsers, apps, etc. and they are open to random pages, almost as if someone else has been using my device. Both devices are locked with strong pin codes, so it is not a local attack.

I can't seem to root the tablet, I have not tried rooting the phone.

Android is definitely not Linux, it is malware with a Linux kernel.

Any solutions to any of this ? I guess I could try to root the devices again.

I have not encountered this behavior on any of my three Android phones or my one Android tablet (which was rooted and which I bricked all by my ownsome).

I have found Android annoying at times and take care with permissions and usage, but have not found it installing and opening programs on its own.

Where did you get this misbehaving beast?

I don't root my devices because it's a risk. Also, I can't trust what the root installer has. It could have it's own malware and back doors. That's just my opinion...

It's possible to install apps to an Android device from the web. If you have the Google account password, you can go to the Google Play store and install any app to any of your devices. Having a PIN on the device has nothing to do with it. You need a strong Google account password, and two-factor authentication enabled. If you haven't done this, you're negligent. As for opening and running apps remotely, it's possible if you have something like Airdroid installed, and you have it running, but this only works on the local network, with access to the Android device. There is a button to recall recently used apps on most devices, either hardware or virtual, and it's possible you're accidentally pressing this and opening previous apps. It takes you to the place you left off in that apps.

The phone is an LG Tribute from Virgin Mobile and the tablet is an iRULU X1 from Amazon.

Malware was found on the tablet using avast antivirus, but it can't be removed.

Maybe?

http://research.zscaler.com/2015/09/...ansomware.html

I was able to disable the malware on my tablet. I'll keep an eye out for more smart devices having a mind of their own.

If they're running Lollipop, I suppose someone could remote in and put a baked-in PIN in and get instant access.

At this point the best chance of getting the malware off is to root it. I would recommend using a tried and true route like Towelroot, Framaroot, or Z4.

Until you get the malware off, I would recommend using Airplane mode to seal off the hacker and only using WiFi when you absolutely need it.

Did Avast indicate a name for this beasty?

It said "Dropper" and then some numbers. Probably some dropper type malware.