1) Was this blessing with candles a part of St John's rite or introduced to the liturgy later?
Almost certainly much, much later. The first evidence of such things dates from some centuries after the death of St John.
2) When was this blessing introduced into the liturgy? Before or after the Council of Chalcedonia?
Likely after, and the particular ceremonial that we have today later still.
3) Is this practice affiliated with the use of candles in Judaism or the Old Testament (menorah or Hanukkah)?
I have no idea. Mother Vassa links them to the Byzantine imperial ceremoinies rather than Jewish liturgical custom.
4) Who decided that the blessing must be added into the divine liturgy right after the Trisagion hymn?
As has been pointed out above, the blessing is performed during
after, the Trisagion. The blessing with the trikiridikiri is also performed after the vesting, at the Lesser Entrance, after the Gospel, the Great Entrance, ordinations, the Communion of the people, and the Dismissal. Who decided on these points I do not know. It is likely the result of the development of the Liturgy over the ages.
5) While blessing the community, the bishop recites some verses of the Psalm the first line of which reads: "O shepherd of Israel, pay attention, you who lead Joseph like a flock of sheep". Why was this particular Psalm selected?
As noted above, the verse quoted is not what is said at this time, but rather, 'Lord, lord, look down from heaven and behold, and visit this vineyard, and perfect that which thy right hand hath planted.' The bishop usually says this while looking up to the icon of the Saviour in the ceiling of the church.
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