If yes, how?
OS: 32-bit Red Hat Enterprise Linux Client release 5.4 (Tikanga)
Not directly. You need to be running a 64-bit kernel to run 64-bit apps.
You may be able to do it via virtualisation though. VMware supports running 64 bit VMs on a 32 bit host if the CPU(s) have support for the required features (not all 64-bit processors do), and I presume some other virtualisation platforms can do this too. You could try install a 64-bit variant of Linux in a VM on running on top of your existing machine's 32-bit OS and run the 64-bit app in there. This might not be at all convenient though, depending on what you are trying to do with the application.
It is possible if you use an emulator like QEMU with X86_64 support. after installing it you should use qemu-system-x86_64 command to run your executable
No. For a start a 64-bit binary will be linked against 64-bit libraries that will not be present on a 32-bit OS.