Romans 9:3 For I could wish that I myself were cursed and cut off from Christ for the sake of my brothers, those of my own race,

What an offer! Paul was willing to give up his salvation (if that were possible, which it isn't) if only his brothers, the Jews would believe. That's pure love!  Moses did a similar thing.

Romans 9:13
Therefore God has mercy on whom he wants to have mercy, and he hardens whom he wants to harden.

God allows a person's heart to be hardened and/or He hardens the heart for His purposes. For example God hardened Pharaoh's heart so that His power and purpose would be made known.
(Exodus 7:3, 9:14)

Romans 10:2
For I can testify about them that they are zealous for God, but their zeal is not based on knowledge.

They were zealous based on the law (legalism) and didn’t have the knowledge of Jesus. This puts us in mind of the Orthodox Jews today.  They were (and many are today) zealous but for all the wrong reasons.

Romans 10:10
For it is with your heart that you believe and are justified, and it is with your mouth that you confess and are saved.

Once we believe and are made right, then we want to live right.

Romans 10:13-15
for, "Everyone who calls on the name of the Lord will be saved." How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them? And how can they preach unless they are sent? As it is written, "How beautiful are the feet of those who bring good news!"

Believers are sent to preach (that word means proclaim) – others hear – others believe – they call on Him – they are saved. The bottom line is... believers are sent and others are saved! Again, we're thinking of Moshe in Israel. He has been sent to Israel, he preaches, others hear, believe, call on Jesus and are saved.

Romans 10:17
Consequently, faith comes from hearing the message, and the message is heard through the word of Christ.

We (Phil and Patti) had similar upbringings.  When we were children, we heard the message. We accepted what Christian adults told us. It brought about a measure of faith in what they were telling us. So that when we accepted Jesus for ourselves we already had a measure of faith. Phil likes to say that we knew Jesus first as a friend before we even knew we needed a Savior.

Romans 10:19
...Moses says, I will make you envious by those who are not a nation; I will make you angry by a nation that has no understanding.

Paul is referring to the Gentiles as "those who are not a nation;"  I wrote this question in the margin of the Bible, "Will Israel be angry and envious because the offer of salvation will be given to the Gentiles?"  That question was answered a few verses down the page in Romans 11 - "salvation has come to the Gentiles to make Israel envious..." 

Romans 10:20
And Isaiah boldly says, "I was found by those who did not seek me; I revealed myself to those who did not ask for me."

We have often used the analogy of a horizontal line. Our life is as a horizontal line. We stay on the line and to eventual destruction until at some point (or many points) God reaches down to us and we reach back to Him. Then we are on the vertical line and on our way to life eternal. (John 3:16-18)

Paul warns the Gentiles of boasting. It seems as if there are some folks today who believe that Israel has been  replaced by the church and all the promises to Israel are now promised to only the church. Not so! Paul warned about boasting that,"Branches were broken off so that I might be grafted in." Later Paul says, "And if they do not persist in unbelief, they will be grafted in."

Our prayer as Believers should be that Israel will not persist in unbelief. That when God reaches down to them (perhaps through people like Moshe in Israel) that they will reach back.