If my husband and I want to be legally separated, can we just draw some papers up ourselves, or even fill out the separation papers we downloaded from ecourt for maricopa county (in arizona), but just have them notarized and witnessed, instead of going through the trouble and expense of filing them through the court? Won't they still be 'legal' ?

Not really, you fill them out and notarize them and file them with the court, then they are legal.

It all depends on what level of "legal" you want, Could you force the other party to the terms of the agreement, normally but marriage is controlled by the government, and issues related to it, has to be ok'ed by the court and/or filed with them to be reconised.