The Kingdom is said to be "of" heaven. Meaning it comes from God and is of God.
The term Kingdom of God is also used. The scope of the Kingdom of God and the Kingdom of Heaven refer to the Millennial reign of the Lord Jesus Christ, but also of the wider aspect of being of the New heavens and earth also. Thus the Kingdom of God is the wider term which involves the Kingdom of Heaven (Millennium) and God future Kingdom throughout eternity. It further refers to God plans in the their entirety from the beginning and into eternity. Heaven itself is the abode of God and involves all God's plans.
Both terms are used in referring to the Millennium, but the term Kingdom of God, refers to the greater extent of God's plan beyond the Millennium.
Thus you are correct with both your statements. In the parables Jesus was addressing the Jews and He as their Messiah was presenting to them the promised Kingdom. Thus in the parable He was talking to Jews and to God's plans for them. We can understand the principles on which the parables are based which are timeless, but the specifics refer to Israel. Always keep Israel and the institution of the local church separate in interpreting God's word. The institution of the local church and the church age was a mystery, not revealed to the Jews and only mentioned by Christ in Matthew 16:18 and not in sight in the Gospels. (Rom. 16:25-26; Eph. 3:1-11; 6:19; Col. 4:3)