Was biblical Abraham a literate

Yes, he probably was literate. The reason for saying that is that the earliest form of writing (Ugaritic and early Akkadian) were developed around 3,500 to 4,000BC and were used extensively in trading.

Abraham (or Abram as he was known in Ur) was wealthy and while he probably had servants to do the recording of his transactions, he would still have needed to be literate to be able to check what was being recorded. He was literate