Could an ant colony have 2 or more "branches" located far from each other (i.e. physically separated but interconnected nests) ? If so, how far is the limit?
Yes, sub- or satellite colonies are common in many species (see e.g. Hölldobler & Wilson, 1990; Debout et al. 2007), and these are then labelled as polydomous species. Subcolonies can either contain extra queens, but sometimes only contain foraging workers. The purpose can be both to expand foraging grounds or as a pre-stage for colony budding. The distance between colonies can differ dramatically between species, but there are cases of supercolonies (especially in the Argentine ant) streching over hundreds of square kilometers (Moffett 2012).
Satellite colonies are also common in e.g. Carpenter ants (Camponotus) and wood ants (e.g. Formica rufa), and when colonies are found inside a house there is often a primary colony somewhere outside the building (see e.g. Ants in the home).