What is the Interpretation of Parimukham in the context of Buddhist Meditation? This seems to have different interpretation and translations? What are the different interpretations and translations and what might be the most correct interpretation according to different line of practice? How is the particular interpretation rationalised?
What are the different interpretations and translations and what might be the most correct interpretation according to the different lines of practice? How are they rationalized?

Here are some:  


  Etymology:
  pari- is a prefix used with the connotation of around, about, all over, or that of completeness. Thus dhāvati means
  'to run' and paridhāvati means 'to run about'; vajati - 'to go/
  proceed' becomes paribbajati, 'to wander about', ie. 'to live the life
  of a religious mendicant'; carati - 'to walk' becomes paricarati - 'to
  walk around, ie. to serve, honour'; gaṇeti, 'to count' becomes
  parigaṇeti - 'to calculate'.
  
  mukhaṃ means primarily and literally 'mouth', by extension 'face' and
  figuratively 'entrance', 'opening', 'brim', then in a more abstract
  meaning 'the front', 'the foremost' and finally 'that which is an
  entrance into something', ie. 'a mean', 'a cause'.
  
  Strictly from the point of view of semantics (ie. neglecting
  contextual information), the following meanings could reasonably be
  derived from the juxtaposition of these two components: around the
  mouth, all over the mouth, completely on the mouth, around the face,
  all over the face, completely on the face, around the entrance, all
  over the entrance, completely on the entrance, around the front, all
  over the front, completely on the front


Note: The above link also has references to commentaries &amp; later Pāḷi literature.  




  Thanissaro Bhikkhu:
  To the fore (parimukhaṃ): The Abhidhamma takes an etymological
  approach to this term, defining it as around (pari-) the mouth
  (mukhaṃ). In the Vinaya, however, it is used in a context (Cv.V.27.4)
  where it undoubtedly means the front of the chest. There is also the
  possibility that the term could be used idiomatically as "to the
  front," which is how I have translated it here.  





  Ānandajoti Bhikkhu:
  Parimukhaṃ means at the front, or perhaps, around the mouth, i.e. it
  is a vague area, not meant to be confined to one particular spot or
  place, which would have been easy to designate if that is what was
  meant (like specifying oṭṭha, the lip). It is of course the
  mindfulness that is important in the practice, not the breathing as
  such, which only provides a basis for the mindfulness.  





  Anālayo Bhikkhu:
  Once the posture is set up, mindfulness is to be established “in
  front”. The injunction “in front” (parimukhaṃ) can be understood
  literally or figuratively. Following the more literal understanding,
  “in front” indicates the nostril area as the most appropriate for
  attention to the in- and out-breaths. Alternatively, “in front”
  understood more figuratively suggests a firm establishment of sati,
  sati being mentally “in front” in the sense of meditative composure
  and attentiveness.  





  Sujato Bhikkhu:
  In the gradual training, sati and upatthana occur together in the
  common idiom parimukhaṃ satim upatthapeti. Here the term parimukha is
  one of those simple words that is so hard to interpret. It modern
  renderings usually use something vague like 'in front'. However the
  phrase frequently occurs in contexts outside of anapanasati, making
  the interpretation 'at the nose-tip', or any literal spatial
  interpretation, unlikely. The Sanskrit has a different reading,
  pratimukha. This has many meanings, among which are 'reflection' and
  'presence'. Both of these would be appropriate in meditative context.
  But the word usually, as here, occurs in close conjunction with
  upatthana, which also means 'presence'. I think here we have another
  example of that common feature of Pali or Sanskrit, a conjunction of
  synonyms for emphasis: literally, 'one makes present a presence of
  presence of mind', or more happily, 'one establishes presence of
  mindfulness'.





  S. N. Goenka: The awareness is established around the mouth,
  the entrance to the nostrils: parimukhaṃ. Certain traditions
  translate this as "in the front," as if the awareness is imagined to
  be in front of the person, but this sets up a duality. Actually you
  have to feel the breath coming and going around the mouth, above the
  upper lip, which is parimukhaṃ.




Additional References:


Parimukhaṁ article with Āgama references  
Footnote 55 of Piya Tan's Study of Kāyagatāsati Sutta  
Dictionary entries