Aramaic Alphabet
Aramaic is a Semitic language which belongs to the Northwest line of Semitic languages. This makes it different from other Semitic languages such as Akkadian, Ethiopic Arabic, Ugaritic and Phoenician. Abraham settled in Aramean territory when he moved to Haran from Ur. Terah and his family would have spoken Aramaic. Rebekah, Leah and Rachel would have spoken Aramaic even though they lived in Canaan after Abraham's move to Palestine. Hebrew is similar in vocabulary and pronunciation to Aramaic and those who have mastered Hebrew find Aramaic easy to pick up. But there are enough differences to make the two languages distinct in their look and sound..
Old Testament
It is not correct to state that all of the Old Testament was written in Hebrew. The latter books of Ezra and Nehemiah have large portions in Aramaic. Ezra 4-7 and Daniel 2-7 were mostly written in Aramaic. Jeremiah 10:11 is also written in Aramaic. Daniel was written in Aramaic because this was the language of the Empire in which he was living at the time of its writing. Ezra was correspondence which was of international interest and so was written in the language of diplomats and kings.
New Testament
In the New Testament times a dialect of Aramaic was spoken and often called Hebrew. Many people in Jesus day spoke this dialect and so you have a few words that have come down to us in Aramaic. Most of the Aramaic we have in the New Testament is recorded for us in the Gospel of Mark. The best known quote is from the cross Eli, Eli, lema Sebaqtani? My God, my God why hast thou forsaken me? Mark 7:34 Another phrase is Abba Father in Romans 8:15
Dead Sea Scrolls
Dead Sea Scroll
Discoveries at the Dead Sea Caves of an Aramaic manuscript, known as Genesis Apocryphon has serious implications for liberal scholars who would seek to date Daniel late during the Maccabean period. When the Aramaic styles are compared they show that the Aramaic of the dead sea scroll had progressed significantly from the book of Daniel giving Daniel a much earlier date. For Further Study See Dead Sea Scrolls
Jewish Usage
Aramaic became the language of the Jews from the late 5th century onward. It was the practice of the Jew in the synagogue to read the scriptures in Hebrew followed by a translation in Aramaic. The second division of the Talmud called the Gemara, the Jewish commentary on the Bible, was entirely written in Aramaic. Also portions of the Midrash and Targum were also written in Aramaic.