In regard to your question about Romans 9:22-23, the Greek for the words you ask about say literally, "vessels of anger that are ripe for destruction." The words "of anger" describe these vessels (in this case people) as being subject to God's anger. The next words indicate why they are subject to God's anger. They are "finished, complete, ripe" for God's eternal destruction in hell.

The word "finished, complete, ripe" is a perfect tense in Greek indicating that the action of their being made "complete" or "ripe" is completed and so they are in the state of ripeness. Who made them ripe for this destruction? They themselves did--like Pharaoh whom Paul discusses in the previous verses. That is why (in the first part of v22) God is ready to punish them as they deserve, but holds back his punishment in great patience (v22b).

The NIV improperly translates this idea with the word "prepared for destruction." The Greek word for "prepared" is used in v23 when Paul is speaking about those whom God has elected, but the word in v22 means "complete" or "ripe." This difference in terms in the two verses indicates that the reason for some being "vessels of anger (v22)" and some being "vessels of mercy (v23)" is not the same. Those who are lost have only themselves to blame because they rejected the free salvation Jesus won for all people. Those who are saved owe God all the thanks because in mercy he led them to accept this free salvation in faith.