If I partition my disk as gpt, can I install my operating system as bios? or will I have a problem? I don't want to reformat my hard drive but I want to install my system with bios boot, otherwise which is better bios or efi?
Confused by some of your use of terms. By "bios", do you mean MBR or whats called "legacy" boot within the bios? Legacy is boot from MBR formatted partition as opposed to GPT/UEFI formatted partition.
Also when you say "partition my disk as gpt" and then say "I don't want to reformat my hard drive"; if you partition, then you are reformatting, and all data on disk is erased.
GPT formatted partitions do include an MBR, thus in theory they should boot a legacy/MBR, but I personally have never done this.
"which is better bios or efi?"- bios (MBR) simpler. EFI more secure (other benefits...). EFI adds an additional security internal to the bios of a variable that connects the booting OS to the actual boot code.
Not sure your current configuration, sounds like legacy MBR, maybe stay with that for now.
Good luck!
please read https://wiki.archlinux.org/index.php/Partitioning#GUID_Partition_Table
as you can see in wiki, you can install BIOS with gpt, without use UEFI. For use UEFI/gpt you MUST format your HDD.