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Check if a machine runs on 64 bit or 32 bit Processor/Linux OS?

Q. How can I check if my server is running on a 64 bit processor and running 64 bit OS or 32 bit operating system?

Before answering above question we have to understand below points.

We can run a 32-bit Operating system on a 64 bit processor/system.
We can run a 64-bit operating system on a 64 bit processor/system.
We cannot run a 64-bit operating system on a 32-bit processor/system.
We can run a 32-bit operating system on a 32-bit processor/system.
Once we are clear about the above 4 points then we can see if our machine have a 64 bit processor or not.

How to check if my CPU is a 64-bit supported processor or not?