The first resurrection is the New Birth (c.f. Ephesians 2:4-5). Once you've got that, the rest falls into place.
Does Eph 2:5 say the same thing as 1 Cor 15:22?
Eph 2:1-3
Also you -- being dead in the trespasses and the sins, in which once ye did walk according to the age of this world, according to the ruler of the authority of the air, of the spirit that is now working in the sons of disobedience, among whom also we all did walk once in the desires of our flesh, doing the wishes of the flesh and of the thoughts, and were by nature children of wrath -- as also the others,
Does that basically say: In Adam all die?
What is, the grace of God that brings salvation? 1 Cor 15 17,18 And if Christ be not raised, your faith is vain; ye are yet in your sins. Then they also which are fallen asleep in Christ are perished.
Is the resurrection from the dead of the seed of David, the grace of God that brings salvation?
Remember that Jesus Christ of the seed of David was raised from the dead according to my gospel: Wherein I suffer trouble, as an evil doer, even unto bonds; but the word of God is not bound. Therefore I endure all things for the elect's sakes, that they may also obtain the salvation which is in Christ Jesus with eternal glory. 2 Tim 2:8-10
I do not believe the first resurrection is out new birth. I believe the first resurrection, 1 Cor 15:23 Christ singular, brought about our receiving the Spirit of adoption Acts 2:32,33 which will result in the adoption, Rom 8:23 & Rom 8:11.
Quickened in Christ.