hi pindemon,
It's better to post your issue/question to Z-Push mailing list to get better support about z-push.
I saw this error in your log:
29/05/2013 20:49:31 [ 1407] [DEBUG] [myemail@domain.com] BackendIMAP->GetAttachmentData('cf7600f9:148:0')
29/05/2013 20:49:31 [ 1407] [ INFO] [myemail@domain.com] StatusException: BackendIMAP->GetAttachmentData('cf7600f9:148:0'): Error, attachment name key can not be parsed - code: 15
29/05/2013 20:49:31 [ 1407] [ INFO] [myemail@domain.com] User-agent: 'Android/4.2.2-EAS-1.3'
And another warning message:
29/05/2013 20:49:31 [ 1407] [ WARN] [myemail@domain.com] Unknown:0 Unknown: SECURITY PROBLEM: insecure server advertised AUTH=PLAIN (errflg=1) (8)