“So in that fashion a variety of Hebrew was still spoken in Israel at Christ’s time...”
All I can find indicates Hebrew was known and used, primarily in religious matters but still Hebrew. The Septuagint met a need but Jesus taught in the synagogues and shows every sign of being familiar with contemporaneous rabbinical discussions, and many of those would have been in Hebrew.
That could well be. The great majority of the Dead Sea scrolls are in Hebrew and some of those should be close in time to the Christian era. However the NT never having been written in Hebrew seems to argue that it was already losing ground as a living language.