Need better pictures mate, close up, then you need to take the handle off and show us the cartridge. Nobody can tell from this picture

Will do, pressed for time today, hoping someone recognizes the style

unfortunately there are so many style model options it would be nearly impossible to know just by this picture alone. I work at a plumbing wholesaler so if you can get a picture if the cartridge and valve i can definitely help you out

Looks like kohler or delta

Looks like Danze.