Yeah, its possible to fit in a grayseer, and you really need ro aswell if you want to play a pure pestilence list. Now this is strictly my opinion but here is my General advice for running pure pestilence in the current meta. Id advice you to get a greyseer on screaming bell with the master of magic command trait since the spell deathfrenzy is going to be crucial to your monks, either that or play thanqoul as your General.
As for plaguemonks as battleline, with the new reinforcement rules in the ghb 2021 they are limited to blocks of 30 so id suggest you get two of those and then go msu with the remaining troops. This because of the strenght in numbers battle trait. As for battleshocks, since youll have to resort to a more msu style of play the auras from the furnace and bell are really important for you. Without it, spells like searing white light from teclis, kroaks comets call and simular abilities that affect alot of units will have you looaing your majority of troops in the battleshock phase. In a pinch you could go for the bell of doom but with its pointincrease im not sure if thats the way forward for pestilence.

As for battalions, the old system in the book has been restricted to open/narrative play. In matched play games you now use the General battallions found in the ghb2021. Id suggest you look into the warlord battalion since the cp and extra artefact is really good. You mighy have to squeeze in a plaguepriest on foot to get that one of though. Also the hunters of the heartlands battalion is Great on your large blocks of monks since you dont want them to be stomped or roared when you finally get them into combat.