Who am 'I'? Verification as to the demarcations of 'Sankhara' It maybe a very confusing question. But I have been contemplating this quite a lot recently. 

Ven. Ajahn Chah preached, as the Lord Buddha once said :


  One who sees Sankhara and is purged of attachment has happiness. Mind is Sankhara. Body is Sankhara. Sankhara is not us or ours. Thus those who see Sankhara are at peace. They see the mind and body not as 'self' but only as 'Sankhara'. (pg.22, paragraph 3) 
   - Excerpt from 'Being Dharma' By Ven.Ajahn Chah


When I contemplate these deep words, I feel that 'Sankhara' means 'things that are conditioned, impermanent, ever changing and not reliable sources of happiness'. 

Wikipedia defines 'Sankhara' as follows:


  Saṅkhāra (Pali; Sanskrit saṃskāra) is a term figuring prominently in Buddhism. The word means 'that which has been put together' and 'that which puts together'.
  In the first (passive) sense, saṅkhāra refers to conditioned phenomena generally but specifically to all mental "dispositions".[1] These are called 'volitional formations' both because they are formed as a result of volition and because they are causes for the arising of future volitional actions.[2] English translations for saṅkhāra in the first sense of the word include 'conditioned things,'[3] 'determinations,'[4] 'fabrications'[5] and 'formations' (or, particularly when referring to mental processes, 'volitional formations').[6]
  In the second (active) sense of the word, saṅkhāra refers to that faculty of the mind/brain apparatus (sankhara-khandha) that puts together those formations.[7] https://en.wikipedia.org/wiki/Sa%E1%B9%85kh%C4%81ra


But when we think even deeper, if both mind and body are 'sankhara', then who is the 'being' within our minds, who travels through this eternity of existence? This 'being' that some refer simply (and quite wrongly) as an 'Āthma' or in other ways as 'existence'? If 'Āthma' or 'existence' is Sankhara, then how does it endlessly exist? Sure it changes from one existence to another, but it is endlessly existing , which contradicts the nature of 'Sankhara' itself, making 'our existence' immortal.

It is like a man travelling from house to house. The house breaks down, but the man is eternally travelling. Who is this man, and how is he eternally travelling, is he is also 'Sankhara'? Shouldn't he also end at some point or the other? In this analogy, the man is the 'existence', and the house symbolizes our body and mind.

I know this is very confusing material, but I consider this site a realm filled with knowledgeable beings. I would find myself very happy to find any number of meaningful replies.

Thankyou!!!
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.