Was Noah still living during Abraham's lifetime?

Answer 1

Yes, according to tradition Noah died when Abraham was 58 years old.
The Torah is silent concerning Noah's later years for two reasons:

1) After the incident with the wine (Genesis ch.9), Noah's ability to influence people was diminished.

2) Some of Noah's descendants who were contemporary with him, such as Shem, Eber, and especially Abraham, eclipsed Noah and greatly surpassed him in righteousness.

Answer 2

According to the biblical account, Noah and all Abraham's subsequent direct ancestors were still alive even when Abraham reached adulthood. For a long time, they must have seemed immortal. Given the Biblical account of Noah's personal experience of God and Noah's patriarchal role in all nations, it should be surprising that during his own lifetime, the entire world had ceased to know God. Although The Bible says Noah was the ancestor of every person in the world, archaeologists have found no evidence of the remaining 350 years of the life of this remarkable man in the records of the Hebrews, Egyptians, Assyrians or any other nation.

Neither Abraham nor any other national leader kept in touch nor sought his advice on any matter. It is as if Noah ceased to exist once he had fulfilled his biblical role of surviving the Flood.