Is it forbidden to be named "Yasir" on the basis that it is the name of the one who casts lots in the Pre-Islamic Era of Ignorance (Jahiliyyah), and has this been reported from the people of knowledge?

There is no objection to naming someone Yasser, and no scholar has prohibited naming with it. Sheikh Bakr Abu Zayd mentioned it in his book "Naming the Newborn" among the male names permissible according to Sharia and language.