The Iranian verbal root dā- is the merger of two entirely different IE roots: *dō “to give” (Greek didōmi) and *dhē “to put in place, to create” (Greek tithēmi). In New Persian the verb dādan always has the meaning “to give”, but there are derivatives of this root with the latter meaning, e.g. dād “that which is laid down, law”; dādār “creator”, dād(w)ar “judge".
dadāiti is 3rd person singular present active, with reduplication of the first consonant (as in the cited Greek words). adā is 3rd person singular aorist active, with the past-tense marker (“augment)” a- (again exactly like the Greek e-).