To begin with, God has never promised us an easy life, but rather the exact opposite. The Bible says:
Enter ye in at the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat: because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it. - Matthew 7:13-14
Remember the word that I said unto you, The servant is not greater than his lord. If they have persecuted me, they will also persecute you; if they have kept my saying, they will keep yours also. - John 15:20
The life of a Christian is hard, filled with trials and tests, sorrows and tribulations. But that does not mean that we are without hope. The Bible says:
And the peace of God, which passeth all understanding, shall keep your hearts and minds through Christ Jesus. - Philippians 4:7
There is joy and a peace in serving God, because we know that God will never give us more then we can endure (1 Corinthians 10:13). Both the saved and the unsaved have problems, trials and tests, but the difference is that we know that God is in control, and that no matter what happens, if we keep on believing and trusting in God, one way or another, God will take care of us. The unsaved do not have this comfort.
Someone once said, "If I lose all my money, my health, and my belongings, but still have my faith, I have lost nothing. If I have all my money, my health and my belongings, but have lost my faith, then I truly have lost everything."
There are many reasons for our suffering, which include teaching us valuable lessons, drawing us closer to God, keeping us humble, teaching us compassion for others, etc.
You asked why when you (or others) pray, it seems that God doesn't answer, in fact, it seems like things just get worse. Sometimes things have to get worse before they can get better. Sometimes God has to break us in order to remake us. Like the potter, God is the potter, and we are the clay. In order for God to make something out of us, He has to chisel away our pride and our sins. The clay doesn't tell the potter how to shape the clay, the clay yields to the potter's hands. In the same way, we must yield to the hands of God as He shapes and remakes us, because we know that He does everything for our own good.
You also asked why God punishes us more then He punishes the unsaved. The Bible says,
And that servant, which knew his lord’s will, and prepared not himself, neither did according to his will, shall be beaten with many stripes. But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him shall be much required: and to whom men have committed much, of him they will ask the more. - Luke 12:47-48