O righteous Father (Πατηρ δικαιε). Nominative form with πατηρ used as vocative (cf. John 20:28), but vocative form δικαιε. Then the righteousness of God is appealed to like God's holiness in verse John 17:11.

The world (κα ο κοσμος). The translations usually slur over the κα as untranslatable in English. Westcott suggests "while" as a sort of correlative. It is quite possible that here κα is almost concessive like "though" and δε=yet: "though the world did not know thee, yet I knew thee, and these knew thee." See Robertson, Grammar, p. 1182 for και--δε--κα and various other uses of κα in John's Gospel.