The day following (tēi epiousēi). As in Act 20:15 which see.
Went in (eisēiei). Imperfect active of eiseimi, old classic verb used only four times in the N.T. (Act 3:3; Act 21:18, Act 21:26; Heb 9:6), a mark of the literary style rather than the colloquial Koinéš use of eiserchomai. Together with us to James (sun hēmin pros Iakōbon). So then Luke is present. The next use of “we” is in Act 27:1 when they leave Caesarea for Rome, but it is not likely that Luke was away from Paul in Jerusalem and Caesarea. The reports of what was done and said in both places is so full and minute that it seems reasonable that Luke got first hand information here whatever his motive was for so full an account of these legal proceedings to be discussed later. There are many details that read like an eye witness’s story (Act 21:30, Act 21:35, Act 21:40; Act 22:2, Act 22:3; Act 23:12, etc.). It was probably the house of James (pros and para so used often).
And all the elders were present (pantes te paregenonto hoi presbuteroi). Clearly James is the leading elder and the others are his guests in a formal reception to Paul. It is noticeable that the apostles are not mentioned, though both elders and apostles are named at the Conference in Acts chapter 15. It would seem that the apostles are away on preaching tours. The whole church was not called together probably because of the known prejudice against Paul created by the Judaizers.