During supper (δειπνου γινομενου). Correct text, present middle participle of γινομα (not γενομενου, second aorist middle participle, "being ended") genitive absolute. Verse John 13:4 shows plainly that the meal was still going on.

The devil having already put (του διαβολου ηδη βεβληκοτος). Another genitive absolute without a connective (asyndeton), perfect active participle of βαλλω, to cast, to put. Luke (Luke 22:3) says that Satan entered Judas when he offered to betray Jesus. Hence John's "already" (ηδη) is pertinent. John repeats his statement in verse John 13:27. In John 6:70 Jesus a year ago had seen that Judas was a devil.

To betray him (ινα παραδο αυτον). Cf. Acts 5:3. Purpose clause with ινα and second aorist active subjunctive of παραδιδωμ (form in -ο as in Mark 14:10 rather than the usual -ω in Luke 22:4). Satan had an open door by now into the heart of Judas.