What do we learn from the Bible's passages about divine mercy, pertinent to bigger issues in Christian doctrine?
1. God is not equal in His giving.
The Lord shows various kinds of mercy to everyone, in various ways and various degrees But He reserves to Himself the right to bestow gifts however He chooses. God is not morally obligated to give everyone everything that He gives others. On the matter of mercy, one size does not fit all.
Paul in Romans 9 addressed the difference between Moses and Pharaoh. God gave Moses gifts (such as revealing His glory, Exodus 33) that He withheld from Pharaoh. In fact, God hardened Pharaoh for his sins, as a step toward judging him.
He gave Joseph gifts, that He withheld from Joseph's cell-mates. He gave David gifts that He withheld from others. This is harmonious with other parts of the Bible about God's freedom.
2. God's ability to direct people enables His mercy.
God’s ability to mercifully bless presupposes that God is in control.
God can orchestrate any circumstance, including the people, in such a way that the one He says shall be blessed will be blessed.
It was God who gave Joseph and Daniel favor in the eyes of others. We don't know how God did it, but the Bible attributes their positive attitudes to the Lord's influence.
Nothing can prevent God from bestowing mercy-gifts on people or nations. Bible examples show God causing someone to be favored by others, or even whole nations to be at peace with others, show that Don't let your faith be crippled by a secular view of free-will.
3. God’s mercy can never be earned.
God’s mercy precedes everything we do.
Many of God’s mercy-gifts are rewards, or God keeping a promise, but other manifestations of divine mercy are prevenient, unconditional, and unilateral. Those mercies are working long before anything we do. God promises His mercy to those who fear Him; but because we're all sinners none of us fear Him (Romans 3:18), so He is mercifulbefore we even meet the condition.
4. Some forms of God's mercy are conditional.
This is a check against hyper-Calvinism, which (among other errors) uses a distortion of the Bible doctrine of divine sovereignty to deny the existence of conditions in God's plan.
One must repent and believe in Christ, to receive saving mercy. Yes, mercy precedes repentance, but repentance is still required. Some expressions of God’s mercy described are bi-lateral, to individuals or nations (usually Israel) who meet the conditions. To say that conditions don't exist in God is the Cause of all things is fatalism and incorrect.
5. God in mercy wants to all to come to repentance.
The doctrine, taught by certain Calvinists such as John Piper, that God has a secret will (say, that God really only wants to save the elect) that directly contravenes His stated will (that God wants all men to come to the knowledge of the truth, 1 Tim. 2:4), would mean that nothing else God says can be trusted. This "secret will" doctrine, which is an attempt to harmonize unconditional election with God's declarations of saving will toward everyone, undermines the trustworthiness of the entire Bible.
God's desire to offer saving mercy to every person is not a mere figure of speech. Whether all who are offered saving mercy ever experience it (note: they do not) are their own stand-alone questions. God wants every person to repent, and receive His mercy.
6. God's mercy is a decision He makes.
Romans 9:18adds the strong ingredient of God’s autonomy, in the question of why and how He shows mercy. Even though God by nature is love, He is neither compelled  nor impelled  to show mercy. God is free, authoritative, and is able to give or withhold mercy as he pleases.
God cannot be forced to be merciful, and He is never “carried away” by some overwhelming inward emotion. God revealed His glory to Moses, not because Moses deserved it, but because God was pleased to do it. God in contrast punished Pharaoh for his willful sins. Pharaoh's punishment was a revelation of God's righteousness. God exercised His royal right to do what He saw fit. God never owes anyone mercy.
 Caused to act by an overwhelming external pressure.
 Caused to act by an irresistible inward force.