Zevachim 65: How Does the Priest Avoid Karet?

The remainder of yesterday's last Mishna teaches us more about the gruesome task of sacrificing the bird for the sin or the burnt offering:

• the offering is valid even if one did not remove the crop, feathers, innards; absorb the blood with salt; anything after squeezing out the blood
• if the head was separated in sacrificing the sin offering or if it was not separated in sacrificing the burnt offering, the offer is disqualified
• if blood was only squeezed from the head but not the body, it is disqualified
• if the blood was squeezed from the body but not the head, it is valid
• all actions must be done for their own sake in a sin offering for the offering to be valid
• a bird burnt offering need not be sacrificed for its own sake
• both a bird sin or burnt offering must be intentionally typical in manner and place sacrificed or they are disqualified but not punishable by karet 
• both a bird sin or burnt offerings are liable to the halachot of piggul - intending to eat or burn the offering beyond its designated time
• sacrifices must be performed in order with their mitzvot:
• one pinches the nape in silence, without disqualifying intent, squeezes the blood intending to eat what should be eaten and to burn what should be burned, at the right time, etc.
• similarly there is another much longer list of erroneous actions (for example, eating an olive bulk of one's offering in the right place and another olive's bulk in the wrong place) that would not be in accordance with their mitzvot
• Rabbi Yehuda disagrees and shares this principle: 
• if the improper intent regarding the time of the action precedes the intent regarding the area, the offering is piggul and one is liable to karet for eating it
• if the intent regarding the area precedes the intent regarding the time, the offering is disqualified and there is no liability to receive karet
• The rabbis disagree:
• in both of those cases the offering is disqualified and does not include liability to receive karet
• if the intent was to eat half an olive-bulk and to burn half an olive-bulk at an inappropriate time or place, the offering is valid because eating/burning do not join together

In their discussion of this Mishna, the rabbis speak of examples of incorrect actions in the process of sacrificing.  Interestingly, one of those problems is someone other than a priest sacrificing a bird.  This is a helpful commentary; I had wondered why, earlier, the rabbis were referring to the "male priest" who would sacrifice an offering.  Why the "male" priest?  Would someone misunderstand and think that the rabbis were referring to a female priest?  As far as I know, wives and daughters of priests were not priests themselves.  Women who were kohenot were subject to guidelines regarding marriage and tithes, etc., but they were not permitted to perform the rites of the priests.  Perhaps this was unclear at some point.  What might this have looked like?

Another conversation is concerned with whether a priest must use his body for all of these tasks or whether a knife might be permitted just to cut the crop.  Further, the Gemara considers how much of the structures within the neck of the bird must be severed by the thumbnail of the priest.