For a detailed arichus on the inyan see Vayaged Yaakov L’leil Pesach
A few points:
1) The Aruch Hashulchan brings the Minhag to say Baruch Haba at the opening of the door
2)It is well known that tzadikim throughout the generations merited to see Eliyahu HaNavi at the Seder, I personally, as a descendent of R’ Mordechai Banet, have a Kabbala that one year at the Seder when the door was opened his ten-year old daughter asked him “Who is that old Yid with the white beard?”. “Shhh” he answered, but it was too late. She passed away that year.
3) Also it’s brought from the Chiddushei HaRim that he marveled at the greatness of the Noda Be’Yehuda that even when he was old and infirm he trudged down many steps to walk Eliyahu HaNavi to the door. The Chiddushei HaRim said that to believe with perfect faith that Eliyahu comes is a higher madreiga than actually seeing him
4) It’s an unfortunate tendency of this generation to ask for a Mekor on accepted Minhagim that Tzadikim have been doing for hundreds of years. Yes, certain shtusim have crept into practice. For example the ‘Muzhinka Dance’ with the broom that originated by the Christians. But anything that we have Mesora on is in itself a Mekor
5) I did not see anything on whether Eiyahu drinks from the Kos. It would seem that if we put a Kos in his honor that he should take a sip. But I’m not certain of that