We say the traditional blessing before taking the bread and the wine. For the bread, "Baruch atah Adonai elohainu melech ha-olam, ha-motzee lechem min ha-arets, Amen. For the wine, Baruch atah Adonai elohainu melech ha-olam, boraeh p'ree ha-gafen; Amen. We do this in rememberance of Yeshua as instructed by Him. When we partake in the bread we remember his body being broken and when we partake in the wine we remember his blood being shed. In no way are we drinking blood in reality or symbolically.
Yes, in our passover celebration, the third cup of the Seder commemorates that Yeshua is the fulfillment of the passover. This 3rd cup is the one that he explained to disciples on the night of his arrest that they should drink in rememberance of Him.