it looks a bit deep in the pot, but might just be the photo. No need to bring it indoors but give it a sheltered site ,, near a hedge, wall etc would do.
Aym, I have two pots of Agapanthus in pots. . . . in sheltered south facing position. They stay out all winter, soluble fertiliser two or three times in spring and have no problems with them.
If it were mine, I'd let it bulk up a bit before splitting, otherwise you'll just have more "punny" agapanthus. Better to have one decent one??
I'd not feed it now. Might just force some new soft foliage.
There are two types of agapanthus - evergreen, which are quite tender, and deciduous which are more hardy. Any idea which it is?
Keep an eye on it over winter then. If all the leaves disappear and you get new shoots in spring, it's deciduous and may well survive in the ground in a sunny spot. If it sort of straggles through the winter, you may need to keep it in a pot and nurse it a little in times of hard frost