I thought the date of Passover was based on the lunar calendar so it will change every year. Because we don’t know the year Jesus died, we don’t know the exact date he entered.
Yes we do.
Wrong, we have DOB 4 BC and of course his death. Some academics argue, but most accept these dates.
We know that Jesus entered Jerusalem on the 10th of Aviv. That is the day when the procession of the national Passover lamb took place, to be taken to the Temple for public sacrifice on the 14th. The national Passover lamb was met by crowds waving palm branches and singing Psalm 118: "Oh Lord, save us (yasha'na), oh Lord grant us success" and "blessed is he who comes in the name of the Lord". Jesus followed the same path to the Temple than the Passover lamb had just taken, met the crowds... well, you know the rest.