I have a new Asus Zenbook here, and honestly I don't know exactly the model and if it has BIOS or UEFI. When I go into BIOS before booting, I see nothing that says UEFI, and it looks pretty much like my BIOS on my old PCs. There is already a Windows 7 installed.
How can I find out if I need to install Grub / Grub2 in BIOS or UEFI mode?
The main question is do you need UEFI? If you don't or don't plan too or just don't know, either, install it as is or deactivate it. There isn't a real "reason" why you should select one or another that goes beyond of what you prefer. Each method has advantage and disadvantages but either way the decision is yours at the end and since you are not interested in dual boot, may as well not do it.
Personally, I don't use UEFI as I don't have a UEFI capable system, if you have one and you don't foresee any troubles, maybe do the jump and use UEFI all the way.
See this page for information on determining your hardware's capabilities and your Windows boot mode. (In brief, if your disk uses MBR partitions, Windows is booting in BIOS/CSM/legacy mode; if the disk uses GPT, then Windows is booting in EFI mode.) You should match your Linux boot mode to your Windows boot mode; if you don't, you risk creating complications for yourself. For more on EFI-mode Linux installation, see my page on the topic and the Ubuntu wiki on EFI.
