There are many, many reasons to doubt that was the case. No doubt Aramaic and Greek were widespread, but there is no reason to think Hebrew was not still in use as an everyday language. Classical Hebrew was the language of the Mishnah (as well as most Dead Sea scrolls). A few hundred years later, Aramaic was used for the Gemara.
Agreed.
However, one must look at those doing the writings. There is little Hebrew from the merchants and regular citizens of the era. Virtually none that I am aware of. The only Hebrew that I am aware of is the religious writings of the religious caste of that era.
Remember though, the Dead Sea Scrolls represent a particular non rabbinical sect. I think that, just as the languages of the Church are first Greek, then Latin, then Church Slavonic, the day to day language of the people was greated more to the vernacular - Aramaic first, then Greek for worldwide communications, much as English is today, and French formerly was.