Having been begotten again (αναγεγεννημενο). Perfect passive participle of αναγενναω, which see in verse 1. Peter 1:2.

Not of corruptible seed (ουκ εκ σπορας φθαρτης). Ablative with εκ as the source, for φθαρτος see verse 1. Peter 1:18, and σπορας (from σπειρω to sow), old word (sowing, seed) here only in N.T., though σπορος in Mark 4:26, etc. For "incorruptible" (αφθαρτου) see verse 1. Peter 1:4; 1. Peter 3:4.

Through the word of God (δια λογου θεου). See James 1:18 for "by the word of truth," verse 1. Peter 1:25 here, and Peter's use of λογος in Acts 10:36. It is the gospel message.

Which liveth and abideth (ζωντος κα μενοντος). These present active participles (from ζαω and μενω) can be taken with θεου (God) or with λογου (word). In verse 1. Peter 1:25 μενε is used with ρημα (word). Still in Daniel 6:26 both μενων and ζων are used with θεος. Either construction makes sense here.