Is there any problem to have a 32-bit operating system and x64-based processor?
No problem at all.
Can my system be updated to x64 based system?
32-bit hardware cannot be upgraded to 64-bit hardware.
If you already have a computer with 64-bit hardware, and you are currently running the 32-bit version of Windows 10, you will have to do a clean install of the 64-bit version of Windows. The 32-bit version cannot be upgraded to the 64-bit version.