How to remove a persistent malware that downloads unwanted apps? Some months ago, I purchased an Azumi cell phone from an official store in a shopping mall in Mexico and subsequently discovered its firmware contains a ton of malware. The malware connects with a server in China and downloads a load of malicious apps which then launch automatically and eventually render the phone so slow as to be unusable. 

I have just done a factory reset for the fifth time and expect it to run smoothly for a few weeks until the problems return. I tried installing a new ROM but it did not resolve the problem, possibly because the malware is hidden inside a partition. 

I am not at all literate with Android, but am willing to learn and do whatever is necessary to fix this phone. Can someone advise or point me in the right direction? 

If I need to root it, how can I do this safely, and how can I locate the offending malware? What diagnostic tests can I perform to learn more about the problem? And if it's easier to flash a new system, what is the most effective way to do this, and where can I locate a reliable ROM?
The app - NoRoot Firewall can be very useful for preventing unwanted malware / adware related app downloads. Cheap phones, tablets (particularly phones off the grey market) typically experience this issue.