Q: I find it hard to determine from the New Testament what applies to the Jews and what applies to the Gentile Church. And can any verses from the Old Testament apply to the Church?
A: Ultimately, the only way we can tell what applies to Israel, and what applies to the Church, is based upon context. A good rule of thumb is that those events which took place before Matthew 12 are primarily addressed to Israel, and those teachings that come after Matthew 12 would be applicable to the wider body. This is not absolutely true, but generally true in most cases.
Concerning the application of the Old Testament, we must determine from the context whether what is said is limited to a specific people, time and place, or is it a universal truth that is always true for everybody. Jeremiah 24:7 is specifically speaking of Israel's national salvation in the future and does not have any direct application to believers today. In context, he is speaking about the prophetic future, when the whole nation of Israel will come to saving faith. In the case of II Chronicles 20:17, he is dealing with a historical event which was a promise limited to a nation (Israel) for a specific battle. It cannot be applied to our war situations today. From both cases, the context determines the meaning, and in the context of both, it is limited to the Jewish people: One is a historical case and one is a future case.
However, there are many other teachings in the Old Testament which are general principles that always hold true. This would include the Book of Proverbs and the Song of Solomon. Things here are not limited to one nation, nor are they limited to the nation based upon the Mosaic Law.
That is why you cannot simply relegate the Old Testament to the Jews of history and the New Testament to the Church today. In both Testaments, there are things which are limited historically, limited to one people, but you will also find things that are universally true for all people.
Two principles are important in understanding Scripture: first, literal interpretation unless the text indicates otherwise; and, second, context, context, context.