I would really like to hear from TER on this one although other TER users' input is greatly appreciated.  

Ever so often I will hear from other people claiming that communicating thru PM is not secure here. Some people claim admin could have access to PM exchanges with others. My question is: do TER admins have access to our private messages without out authorization

... by accepting TER's Terms of Service Agreement.

The way I read TER's privacy policy (see link), TER reserves the right to use your personal information under certain circumstances:

"CONFIDENTIALITY AND SECURITY OF PERSONAL INFORMATION. Except as otherwise provided in this Privacy Policy, we will keep your Personal Information private and will not share it with third parties, unless such disclosure is necessary to: (a) comply with a court order or other legal process; (b) satisfy our legal obligations to cooperate with law enforcement or other investigating agencies; (c) satisfy any laws or regulations, or, governmental or legal requests for such information; (d) protect our rights or property, or the rights or property of others; or (d) enforce our terms of service Agreement."

Note especially the last exception. How I read that is, if you are suspected of violating TER's terms of service agreement, TER Admin could access personal info to investigate..  PMs aren't specifically mentioned anywhere in the Privacy Policy, but I think it's reasonable to conclude they are considered "personal information".

It's not clear from the privacy policy that PMs are stored in encrypted form.  They are transmitted to/from TER in encrypted form if encryption is enabled on your device, as it is on mine (i.e. HTTPS).  If PMs are not encrypted on disk, anyone with access to the server including TER Admin could potentially read them.   TER states that they take measures to protect data, but as we all know almost any server can be hacked with enough skill and effort.  

It would be great if Admin would confirm or correct my analysis on this question.

I believe their software is coded to flag certain words and will identify any such message for checking.  So do not, for example, mention other competitive sites.  I have no idea what other subjects set off their alarm bells.

YES..

It is their site, not yours or mine.

Of course assume anything you send by pm will be read.

Switch to email as only our government will read those.

When you sign up with TER (required before you can use PMs), you must indicate that you agree to TER's Terms and Conditions, which include its Privacy Policy.  Those Ts & Cs give TER authorization to access your personal information under certain circumstances.  

For myself, I assume any PMs I send COULD be read by Admin, not that they necessarily WILL be read.  They'd be bored to tears if they read every one of my PMs.