I would like to know according to my motherboard (Gigabyte GA-P35-S3) if the BIOS are "placed" on a socket which is inserted (and can get plugged out of) to the motherboard, or is it soldered, which means, a motherboard replacement in case of BIOS replacement.
Is it something that I can check by a software, or it should be by opening up the case?
Your BIOS EEPROM is soldered directly on to the board. You don't have a socket for the EEPROM on your board. Don't even bother trying to replace the EEPROM; it takes skill and some specialized equipment. Most if not all BIOS EEPROMs are now soldered on to the board to reduce cost.
Look to the right of the second PCI slot up from the bottom of the board, the chip will be soldered there(its in the manual), As said, it can be removed, but its hard and chances are you will kill the board if you make one slip.