Who am 'I'? Verification as to the demarcations of 'Sankhara'
who is the 'being' within our minds, who travels through this eternity
  of existence?


'being' is simply a label given to nama-rupa. There's no being within the mind. It's like asking "what is the car within the car? Is it the engine? Wheels? Frame? Seats?". No such thing! 'Car' is simply a label given to a certain arrangement of all that.


  Who travels through this eternity of existence?


Nobody! A being traveling through a Samsara is simply used in the metaphoric sense to give teachings at conceptual level. In reality, it's just Paticcasamuppada.

Sankhara paccaya Vinnana - Dependent on Karma consciousness arises


  Sure it changes from one existence to another, but it is endlessly
  existing


What do you mean by 'it' here? Is it Nama, or is it Rupa? A single Rupa unit only lasts for 17 thought moments. The next Rupa arising is not the same as the previous. Nama vanishes even quicker. So what exactly is endlessly existing? 

"It existing" here is simply a false view of reality about a Sanna(perception) caused by contact at the sense doors. Ignorance covers up impermanence, so instead of taking Sanna as just Sanna that rises and dies, we take Sanna as something existing. 

Remaining questions are based on the above mentioned.