I tried removing php-mbstring from easyapache4 and installed it again but still no luck.
I tried to find any errors generated by ProjeQtOr. Cpanel by default set it up like wherever error occurs it logs it into error_log file in folder but there is no such file showing any kind of error.

Is there any way we can check log to find out what is going on? Also I doubt my php.ini config is not according to ProjeQtOr requirment, so is there any way I can find out which config settings needs to be changed?

You must check projector log file in projeqtor/files/logs and apache error log file (may content explanations)

Okay, finally found error in logs, I am receiving following error most of time.

Error on SqlElement to get 'idTargetVersion' for Class 'Activity' : field 'idTargetVersion' not found in Database.

Do you have some customized screen ?
If so, get to /model/custom, open Activity.php file and remove line with idTargetVersion (it should be something like public $idTargetVersion;
(this field was renamed to idTargetProductVersion)

I commented line public idTargetVersion from /model/custom but now i am receiving following error

Error on SqlElement to get 'idTargetVersion' for Class 'Activity' : field 'idTargetVersion' not found in Database.

I did not see updated field name idTargetProductVersion. I also tried clearing cache.
The database version and application version is 6.0.6.
One more thing I do not have any kind customization done in software as per my knowledge so I believe we do not have customized screen so what to do?
In /model/custom I have two files which are _securityCheck.php and Activity.php

If you do not have customization, just remove /model/custom/Activity.php
(rename it for instance as Activity.php.sav to keep trace, in case of...)