I downloaded the qt-opensource-linux-x86-1.6.0-5-online.run (32 bit) and ran it.
QT Setup Wizard appeared and during installation, I am getting “Hash verification while downloading failed.
it stuck when downloading the “1.6.0-5installerbase-linux-x86.7z” for component:Maintenance Tools
I tried many times and I am getting the same error.

Any idea on what do I need to do?

From the directory where you got the "qt-opensource-linux-x86-1.6.0-5-online.run" file also download the "md5sums.txt" and verify the hash before you run the installer?

there was only qt-opensource-linux-x86-1.6.0-5-online.run" file to download and no "md5sums.txt".

I found a larger package to download which was
Qt 5.3.2 for Linux 32-bit (449 MB) (Info) and managed to install it without error.

in the Application/Programming menu, I have a QT Creator (opensource). But when I click on it nothing happening!

I tried manually to run the qtcreator but I am getting the following errors;

[root@rpcztc bin]# ./qtcreator
Failed to load core: /opt/Qt5.3.2/Tools/QtCreator/lib/qtcreator/plugins/libCore.so: Cannot load library /opt/Qt5.3.2/Tools/QtCreator/lib/qtcreator/plugins/libCore.so: (/usr/lib/libstdc++.so.6: version `GLIBCXX_3.4.14' not found (required by /opt/Qt5.3.2/Tools/QtCreator/lib/qtcreator/plugins/libCore.so))

I already used yum install mesa-libGL and yum install mesa-libGL-devel

First of all you should not (need to) run such things as root and secondly it seems this package was not compiled for the glibc version your Linux distribution offers you right now. Note messing with glibc is not advisable. See if your Linux distribution offers any alternatives, else it would be easier to find out what Linux distribution the package was compiled for (or even compile the package yourself).