Luke 23:34 seems to fulfill Isaiah 53:12, with Christ praying for those putting Him to death. Praying for our enemies is both commanded, Matthew 5:44, and is given as instruction here by example.
The risen Christ is our High Priest, He stands before God and intercedes on our behalf, Romans 8:34.
The question asked in post #3 is a good one. Hebrews 7:25 appears to indicate Christ intercedes for those who draw near to God "through Him." And these would not be lost sinners separated from God due to being in a spiritually dead state, but those who have been made alive, together with Christ - those whose faith God has credited as righteousness and spiritually placed "in Christ."
I think it would be a mistake to think Christ's intercession providing salvation, is meant by Christ praying for the lost. Apples and oranges. So while I think it is correct to say Christ only "intercedes" on behalf of the elect, as presented in Hebrews 7:25, it would be wrong to say Christ did not "intercede" on behalf of the lost when He laid down His life as a ransom for all.