Given the piercing nature of the byakugan; it's ability to seethe chakra network of people, chakra flow, and chakra for ninjutsu and genjutsu. Is it possible?
I wish they showed more about the byakugan, like if they'd been able to read the Uchiha slabs, but I feel like they pretty much covered the extent of it in the first arc
Yes because manga stated the Byakugan's insight is greater than the Sharingan's, and the only other dojutsu superior to Sharingan is Rinnegan, and Hamura = Hagoromo, so Rinnegan = Byakugan. So yes, it can see Limbo but only with Hamura's chakra.
It took Naruto's sensing in RSM and Sasuke's perception with Rinnegan to detect them. Absolutely not, otherwise a Hyuuga should be able to see them when Madara first used it.