For this they wilfully forget (lanthanei gar autous touto thelontas). Literally, “for this escapes them being willing.” See this use of lanthanō (old verb, to escape notice of, to be hidden from) in Act 26:26. The present active participle thelontas (from thelō, to wish) has almost an adverbial sense here.
Compacted (sunestōsa). See Paul’s sunestēken (Col 1:17) “consist.” Second perfect active (intransitive) participle of sunistēmi, feminine singular agreeing with gē (nearest to it) rather than with ouranoi (subject of ēsan imperfect plural). There is no need to make Peter mean the Jewish mystical “seven heavens” because of the plural which was used interchangeably with the singular (Mat 5:9.).
Out of water and amidst water (ex hudatos kai di' hudatos). Out of the primeval watery chaos (Gen 1:2), but it is not plain what is meant by di' hudatos, which naturally means “by means of water,” though dia with the genitive is used for a condition or state (Heb 12:1). The reference may be to Gen 1:9, the gathering together of the waters.
By the word of God (tōi tou theou logōi). Instrumental case logōi, “by the fiat of God” (Gen 1:3; Heb 11:3 rēmati theou).