How does Orthodoxy view the Old Testament Torah practice such as Sabbath-keeping and prohibition of eating certain animal meats (Lev 11)?
The word 'Sabbath' means rest, and the commandment of keeping this weekly rest for the Lord is still fulfilled. Since the early Church, the disciples replaced the day of the Sabbath (Saturday) by the first day of the week. We read in the Holy Book of Acts "Now on the first day of the week, when the disciples came together to break bread" (Acts 20:7). This is to commemorate the day of the Resurrection of our Lord Jesus Christ "Now when He rose early on the first day of the week" (Mark 16:9). On Friday, Our Lord, Jesus Christ rested after having offered His blood for our salvation by paying the debt of sin in full on the cross. On Sunday, He released us from death by His resurrection and victory over it. Thus, Sunday became the real rest of the Lord.
The prohibition of certain meat: In a vision St. Peter (Acts 10:9-16) saw a great sheet full of all kinds of animals, wild beasts, creeping things and birds and commanded him to kill and eat. Following Leviticus 11, St. Peter objected. However, the Lord, three times, admonished St. Peter's resistance with the words, "What God has cleansed you must not call common". Our Lord Jesus Christ taught us "Not what goes into the mouth defiles a man; but what comes out of the mouth, this defiles a man" (Mt 15:11).