I would like some information about prayer, such as what to pray for and why prayer is important?

Prayer is the means by which the Christian can voice to God his fears, concerns, pleas for help, and thanksgiving for blessings received.  Though sometimes a prayer may only center on one thing, it may also center on several.  Perhaps the following acrostic will help in knowing what the elements of prayer are - ACTSS. 

A - adoration; God needs to be exalted in prayer, acknowledged as the supreme being, the only true and living God. 

C - confession; we must acknowledge our sinfulness and our sins to God.  He cannot not forgive when we do not ask to be forgiven. 

T - thanksgiving; we must thank God for His multitude of blessings. 

S - supplication; these are our requests, whether personal or on behalf of others. 

S - submission; we must submit ourselves to the will of God.  He answers every prayer, it is just that sometimes He says yes, sometimes no, and sometimes wait.  Some other things to help you in your praying are as follows:

1) Remember that the Holy Spirit will help you in your prayers, Romans 8:26. 
2) Ask according to God's will, 1 John 5:14-15. 
3) Spend time alone with God, Luke 5:15-16. 
4) Live obediently, 1 John 3:22. 
5) Pray with confidence, Hebrews 4:16. 
6) Pray in faith, James 1:6. 
7) Pray with expectancy, Mark 11:24.

Where is the first place the word prayer is in the Bible?

Genesis 20:7, 17

Why do we pray, and how is it possible that prayers are answered?

We pray because we are instructed to pray in the scriptures. Jesus said,
"that men ought always to pray, and not to faint (or give up)". Luke18:1.
Jesus sat the example for us in that sometimes he prayed all night. If he
considered it a necessity to pray how much more then should I pray. There
are more commands to pray in the scriptures than just about anything else we
are urged to do. The apostle Paul said, "Pray without ceasing" (1 Thessalonians 5:17). Since God is omnipresent, omniscient, and omnipotent
he can hear us wherever we are so we do not have to worry about his ability
to hear our request. 

I suggest you find a concordance if you do not have
one and look up all the scriptures on the subject of prayer. You can find
one at almost any church library that you could use, or they can be
purchased at reasonable cost in religious bookstores. A topical Bible would
be ideal as they list the scriptures on the subject and have most of them
written out. I believe you will find this approach most helpful as you
study the subject of prayer.

Where in the bible is the prayer of Japhaz located?

I find no such person mentioned in the scriptures. However there is the prayer of Jabez. It is found in 1 Chronicles 4:10.