Difficult questions to answer.

Gnosticism is a term coined by later scholars to describe various groups, who would have described themselves as Gnostics, i.e. those who were seeking gnosis - direct spiritual knowledge/experience. So they would not have been aware of that term.

Several of these groups were openly Christian, but had radically different interpretations, and were condemned as heretics and persecuted by the Church. Some of their texts were discovered at Nag Hammadi in 1945. The best known is the Gospel of Thomas, which contains many supposed sayings of Jesus, some not found in the New Testament.