questions about heimer and the new masteries

i have many questions that i have been curious about for quite a long time i have searched for answers on the internet but can never find anything helpful. #1: if i took the mastery feast would my turret killing a unit heal me even if i didnt kill it myself? .how would battle trance interact with my turrets?? like would the bonus damage be transferred to them and would the towers dealing damage count as heimer being in combat and build up the damage??? Also does the mastery sorcery increase the damage of every turret hit by 2 percent? And if i had green fathers gift and I walked into a brush as heimer would that mean that any of my turrets next attacks to an enemy champ would deal bonus damage without me even hitting the enemy? And lastly, if i took grasp of the undying would turrets attacking and me not doing anything count as me being in combat and prep the bonus damage for my next auto?? any help is appreciated and thanks! (if you're not sure about anything or are just guessing answers then please don't comment without telling me that what you're saying may not be true)