Here Paul uses a double negative to emphasize the positive. You can translate this in a positive form. Alternate translation: "I very much want you to be informed" (See: [[rc://en/ta/man/translate/figs-doublenegatives]])
Paul does not want the Gentile believers to think they are wiser than the Jewish unbelievers. Alternate translation: "so that you will not think you are wiser than you are" (See: [[rc://en/ta/man/translate/figs-explicit]])
This is the mystery that Paul referred to earlier in the sentence. This can be made a explicit. "A partial hardening" is a metaphor for many of the people remaining stubborn. Paul said this because some of the Jews stubbornly refused to trust Jesus. Alternate translation: "This mystery is that a partial hardening has come upon Israel" or "Many people of Israel remain stubborn" (See: [[rc://en/ta/man/translate/figs-explicit]] and [[rc://en/ta/man/translate/figs-metaphor]])
Here "full number" means the amount determined by God. It does not mean all Gentiles. Alternate translation: "until the number of Gentiles determined by God" (See: [[rc://en/ta/man/translate/figs-explicit]])
This is a metaphor meaning to be saved or to become a Christian. Alternate translation: "is saved" or "believes in Christ" (See: [[rc://en/ta/man/translate/figs-metaphor]])