Some questions about pushing Deer...

Hello all, I have a few questions on Deer pushing... I am aware of the basic build orders and I am looking for some info about pushing Deer... ​B4 going to Deer, about Boars, if I see a Boar before vil no 7, can I go for it with vil no 7 or wait for vil no 10... I don't usually Drush so I am not in a hurry to increase my wood count... Pretty sure there is no risk here,but still trying to confirm... ​Now, coming to Deer... If my Scout walks into a Deer patch, do I go for it, provided of course, that it is a pushable distance? My question is specifically if you have a Boar scouted... Pushing both Deer and Boar is almost impossible... But, at the same time, moving the Scout away and then sending him back wastes valuable Scout time... ​Finally, what is the issue in pushing Deer to the mill? I see the pro players always push Deer to the Town Centre even if the Mill is nearer... Drop off is one problem... But, even in late Dark age when the it's already enough food under TC, they still go to the TC...

I know pushing Deer is not mandatory, but I would like to have it in my kitty just in case...