now realm wrote:I've checked from the pali canon suttas and found that cattasa parisa is referring to the four fold assembly which is the 4 pairs 8 individuals i.e. sotapanna sakadagami anagami arahant and is also referred to as ariya sangha.
You seem to be confusing the cattāri purisayugāni (four pairs of persons) with the catasso parisā (four assemblies). The former is the ariyasangha, comprising sotāpannas, etc., while the latter are the assemblies of monks, nuns, laymen and laywomen.
now realm wrote:I also cited another sutta i.e. parinibbana sutta under the heading 'Mirror of the dhamma' stating that the Order of the disciples of the noble one - the 4 male pairs 8 male individuals.
Like the English word 'man', the Pali 'purisa' sometimes means a male person and other times a person of either sex. In the context of "four pairs of purisas" it is the latter, with both sexes included.
now realm wrote:It looks to me like the Order of the Sangha is headed by the bhikkhus Sangha. Is that correct?
If we're speaking of the ariyasangha, then it's not really "headed" by anybody; it's an invisible church, so to speak, not a known community of people that one can point to. If we're speaking about the monastic sangha, then the order of nuns is subordinate in certain respects to the order of monks.
now realm wrote:Say, if I'm a buddhist who take refuge in the triple gem but not yet a stream enterer, which sangha do I belong to?
In the Theravadin usage of terms you wouldn't belong to any sangha but to the upāsaka-parisā or upāsikā-parisā, depending on your sex.