New to MtG here.
Assuming I pay the one, tap the BiaJ and it has the appropriate number of counters on it, will this let me play sorceries during my opponent's turn?
>>46318593
Yes.
>>46318593
No, it still requires casting.
>>46318593
Yes you can
Yes, an activated ability may be used any time you could play an instant.
>>46318593
Yes, it allows you to cast a sorcery spell during your opponents turn.
The ability says you can cast a sorcery, so you can cast a sorcery. Card text always overrides the rules.
Note that it does NOT allow you to cast spells with specific timing restrictions in their game text. A spell that says "cast only during combat" for instance can only be cast during combat, even if you activate Brain in a Jar with the right number of counters out of combat.