Is it wrong to quote the Bible in your prayer? If yes, why, and if no, why?
Nowhere in the Bible does it forbid one to quote Bible passages in prayer. As long as your prayers are sincere, humble, with faithfulness, fervent, watchful, praising and thankful, quoting Scripture is not inappropriate.
As an example, this prayer was offered up when Peter and John were released from prison:
"So when they heard that, they raised their voice to God with one accord and said: "Lord, You are God, who made heaven and earth and the sea, and all that is in them, who by the mouth of Your servant David have said: 'Why did the nations rage, and the people plot vain things? The kings of the earth took their stand, and the rulers were gathered together against the LORD and against His Christ.' For truly against Your holy Servant Jesus, whom You anointed, both Herod and Pontius Pilate, with the Gentiles and the people of Israel, were gathered together to do whatever Your hand and Your purpose determined before to be done. Now, Lord, look on their threats, and grant to Your servants that with all boldness they may speak Your word, by stretching out Your hand to heal, and that signs and wonders may be done through the name of Your holy Servant Jesus"" (Acts 4:24-30).
There are two passages quoted in this prayer: Nehemiah 9:6 and Psalms 2:1-2.
However, since man has a tendency to be verbose, problems can arise when one says long prayers that are not in sincerity. Jesus stated to the apostles,"And when you pray, do not use vain repetitions as the heathen do. For they think that they will be heard for their many words. Therefore do not be like them. For your Father knows the things you have need of before you ask Him" (Matthew 6:7-8). Avoid rote prayers like denominations use. For example, many denominations misinterpret Matthew 6:9-13 and Luke 11:1-4 and pray the exacting wording of this prayer. In these passages, Jesus is merely giving a sample prayer to illustrate how his disciples should pray. It was not meant to be recited word for word in every prayer, that would be an example of vain repetition as Jesus stated in earlier in Matthew 6.