Unlike Easter, the Passover could fall on any day: the Passover lamb was selected on the 10th day of the first month (Ex 12:3), to be kept alive until the 14th day, when it was killed at twilight (12:6).
In the Law (Lev 23:5-6), the Passover Day itself (14th Nisan or Abib) was followed by the seven days of unleavened bread (15-21 Nisan), but the whole feast seems to have been grouped together under a common name in the New Testament, "the feast of the Passover and the unleavened bread".
The "preparation of the Passover" (John 19:14,31-32) was the day on which the lamb was killed, the preparation for the seven days of devotion that were to follow. There is no appointed feast on the 14th.
Jesus said the Son of Man would be three days and three nights in the earth. The following chart shows how this could be so, counting from before dark on Thursday to before dawn on Sunday.
For most of us, when the clock strikes midnight, it announces the start of a new day, but the Jews start each new day at sunset. The woman who saw where Jesus was buried bought spices when the Sabbath was past (i.e. after sunset) and went to the tomb at their first opportunity. They could not go on the Saturday (the weekly Sabbath), nor on the Friday (if it were the 15th, being the first of the seven days of devotion), for there was no work done on that first day (Lev 23:7). This would be the special Sabbath you refer to.
The Pharisees appealed to Pilate to set a guard for the third night (Matt 27:63-64). They were taking precautions against the stealing of the body to fulfil his words, "After three days I will rise again."
The death of Jesus was the sacrifice to which that of the Passover lambs had always pointed forward, and it is most likely that Jesus died at the very time the lambs began to be killed in the Temple. This would mean that the Last Supper was held on the evening before that of the Jewish Passover meal, and was a new institution for his disciples.
Some supporting evidence:
Dr Roger Rusk, professor of physics at the University of Tennessee, used tables of new and full moons from 1001BC to 1651AD, calculated on a computer at Princeton Institute of Advanced Studies, and concluded that the 14th day of the month Abib, when Jesus died, came on Thursday in the year AD 30 ('The Vatican Papers', p189 by Nino Lo Bello)
Occurrences of 14th Abib in the years AD24 to 33 have been shown to be:
Mosheim's "Ecclesiastical History" (pp 57-58) shows that from apostolic days until the early 4th century the eastern churches were not in agreement with Good Friday, as observed in the western churches:
|"The Christians of the Lesser Asia kept this feast (of the death of Jesus) on the fourteenth day of the first Jewish month (Abib), at the time that the Jews celebrated their Passover, and, three days after, commemorated the resurrection of the Triumphant Redeemer. They affirmed that they had derived this custom from the apostles John and Philip."|
The subject is quite complicated, and it is hard to give a brief and comprehensive explanation. It is not something I would be dogmatic about, but it does seem possible to harmonise the various NT verses with this explanation.