Viewing prayer as a response to God is part of the theological reflection that marks the contemplative life. One prays not only for needs, but in order to acknowledge things that God has done through Providence without even having been asked. Indeed, God knows our needs better than we do ourselves. Therefore, one needs to regard all things as suitable objects of prayer. There is nothing too trivial to bring to God in prayer.
Prayers can be individual and corporate.
The Bible is also full of individual prayers, and Jesus spent a great deal of time in prayer. One prays to the Father, through the Spirit, and in the name of the Son. The desired result of all prayer should be the fulfillment of God's goals, not ours. Since it is our job to co-labor with God, prayer requests should be framed in a context of obedience, the petitioner rejoicing in what God is doing in the world and seeking ways to further His agenda for the Creation. Jesus came to suffer and die for that redemptive agenda, so God's plan for us will certainly include suffering and serving love.