Hi Love Gods Word:
Hope my rather succinct answers to your questions help.
Q1) Scriptures define the church as Gods people or the followers of Jesus. In the early days there were ony 2 "denominations" The Jewish wing and the gentile wing of Christians. But they all made up teh body of Christ.
Peter was the Apostle to teh Jews, Paul to teh Gentiles and James led the Jerusalem church! As Paul said in corinthians we are the body of Christ.
Q2) God does not recognize "sects" and "denominations" as shown here:
1 Corinthians 1:11-13
King James Version
11 For it hath been declared unto me of you, my brethren, by them which are of the house of Chloe, that there are contentions among you.
12 Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ.
13 Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul?
The true church is comprised of all of those who have been born again and are followers of Jesus! There are many "good" churches and "bad" churches. Many denominations have devolved generally speaking into what Paul said:
2 Timothy 3:5
Having a form of godliness, but denying the power thereof: from such turn away.
Q3) for the New Testament- gods people are defined of all those both Jew and Gentile who belong to Jesus!
Q4) In the New Covenant Gods Israel is those Jews who have received Jesus as Messiah!
Paul showed this clearly in romans.
Rom. 9: 6 Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:
Romans 11
King James Version
11 I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin.
2 God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? how he maketh intercession to God against Israel saying,
3 Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life.
4 But what saith the answer of God unto him? I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal.
5 Even so then at this present time also there is a remnant according to the election of grace.
Galatians 6:16
And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God.
Paul is asking for peace to two groups- those who walk according to this rule and to the Israel of God!
So The Israel of God in the new covenant are those remnant that are faithful and accept Jesus as Messiah in every generation.
Q5) Gods church is the same definition as teh church it is comprised of all believing Jews and gentiles who form one body- the church.
Hope this helps.
BTW I believe you are way off in counting denominations. Most sources who deal with these things put the number of denominations around 13,000 which is still way too large!