Not everything has to be in the bible, the rabbis were given authority over matters and even Jesus recognized this in Matt 23, despite calling them hypocrites. Some of the things called "traditions of men" were modern innovations that were not even approved of by rabbis, like the korban abuse. Deuteronomy 17:11 states unclear matters/matters not in the torah are to be settled by JUDGES, this is the Jewish basis for rabbinical authority, as far as the Karaites go--They were probably a post 2nd temple movement, there's no reference to them in the Hebrew bible or the Christian at all. The the way the New testament DOES accept some rabbinical rulings/"traditions" of law like in Acts 15 where eating strangled animals is forbidden to gentiles--this is never explicitly written in the Torah.
The Christian view of purgatory is in 1 cor 3:15 "shall be saved as
though by fire" which is the chief verse used, others can include
MAtthew 12:32 "shall not be forgiven in this age or in the age to come",
Matt 5:26 "until the last farthing" and 2 Thess 1 where Onesiphorous,
seems to be dead, and is prayed for by Paul.