I have to agree, Atlas joint is preferable, if you are competent & the animal is not too mobile.unless you have a lot of experiance i wouldnt consider the atlas joint , you may end up looking a bit amaturish ,just my opinion but if the only options are cutting throat or atlas i would opt for the former ,i no atlas is very quick but if your not very competant play it safe !
Messy and not quick.
Would be my absolute last choice. I'd rather wait for someone better equipped. Unless the animal was unconscious you could be guilty of casuing unnecessary suffering.
Using a folding knife puts you at risk. You cannot just carry a fixed blade.
Totally agree with Apache.
Cutting the throat will not necessarily immobilise a deer, it may in fact encourage flight.