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>>is the cup of blessing St Paul talks about in 1 Corinthians 10 a participation with the blood of Christ, yes or no?<<

I don't think it means what you think it means.

koinónia - spiritual fellowship, a fellowship in the spirit. [http://biblehub.com/greek/2842.htm]

1 Corinthians 10:16 The cup of the blessing that we bless -- is it not the fellowship (koinónia) of the blood of the Christ? the bread that we break -- is it not the fellowship (koinónia) of the body of the Christ?

2 Corinthians 13:14 the grace of the Lord Jesus Christ, and the love of God, and the fellowship (koinónia) of the Holy Spirit, is with you all! Amen.

Galatians 2:9 and having known the grace that was given to me, James, and Cephas, and John, who were esteemed to be pillars, a right hand of fellowship (koinónia) they did give to me, and to Barnabas, that we to the nations, and they to the circumcision may go,

Philippians 1:5 For your fellowship (koinónia) in the gospel from the first day until now;

Philippians 3:10 That I may know him, and the power of his resurrection, and the fellowship (koinónia) of his sufferings, being made conformable unto his death;

Did you also literally suffer with Christ?