Thank you tll for tip.
I change the mail box types from qmail style (MailDir) to Mbox and now all of the users have their own file of messages in /var.
My first problem is that a given user,say Jim is able to send any message to outside world,for instance he may send email to firstname.lastname@example.org
but he is not able to receive messages incoming.
I inspected the problem and figured out that:
The sender message from Yahoo got a "Quota Exceeded" error message in response to sent mail as an undelivered one.
*The only account experiencing no problem is root .Root may receive incoming messages ,which seems natural due to no limit regulations for her.