These are very strange symptoms you are experiencing. If you hadn't replaced the phone (twice), I would recommend a full Factory Data Restore. However, since the phone has been replaced and you're apparently experiencing the same symptoms I would point to one of several possibilities.
First, are you using the STOCK MOTOROLA Charging Block and STOCK MOTOROLA cable? If not, it is a known problem with many third party chargers and cables (even those of reputable manufacturers), causing what is known as "ghost typing", where the digitizer senses minute variations in voltages coming from the charger and interprets them as touches on the screen. This can open apps, take photos, play media, text people and initiate phone calls to contacts or to random phone numbers. Especially the fact that the texts it sends is "jibberish" leads me to believe it's either a third-party charger or a defective one, since when "ghost typing" it does so with completely random letters and numbers. To see it in action (as I have), you'd think the phone was possessed, or being controlled by "a ghost", hence the name.
Here's a link to a very old thread (there are plenty of others like it), describing the issues you mention.
http://www.droidforums.net/forum/tech-issues-bug-reports-suggestions/4081-rogue-droid-huge-issue.html
Another potential cause of "ghost typing" is dirt, oils or moisture at the edges of the glass screen between the glass and where it meets up with the metal bezel (surrounding external metal frame). This was a huge problem with the OD Droid, but seems to be almost a non-issue with the newer generation digitizers. Similar to the voltage fluctuations in the non-stock chargers, the digitizer detects the dirt, oils and moisture as changes in the screen capacitance which is how it determines where you touch the screen. This changing capacitance is interpreted as your finger making those touches and results in the same symptoms you describe.
To fix this problem, Isopropyl Alcohol on a cotton swab can be used to clean the screen, and to get the dirt and oils from the edges, a piece of thin rigid plastic, the type used in theft-resistant packaging, cut to a point can be used to dig out along the edges of the glass.
Finally, if you are using the STOCK CHARGER and STOCK CABLE, then I would point to a software app that you've installed which may be infected with a virus, or which is incompatible with your phone and causing the strange symptoms. Symptoms of the nature you describe just don't manifest themselves - especially across three different phones (the original and 2 replacements). There has to be a cause.
Either way, I have to point to the user's actions as the cause since the statistical odds of 3 phones in a row all exhibiting the same, unique, completely inexplicable and highly unusual symptoms is monumental. If these phones exhibited those symptoms with others, there would be information related to it on our and others' forums. I can't find anything remotely similar in my searches, other than the known issues related to third-party chargers and screen edge dirt.
Sent from my A210 using Tapatalk HD
