The whole thing about holding hands being a normal thing for girls immediately followed by Luna and Kohime doing it while going for lunch is hilarious.
Even Ramune is kind of expensive, with the varities of it Walmart sells (Original, Melon & Strawberry) being $2.22 for a 6.76oz/200ml bottle. You can get a 2 liter brand-name soda for $2.69. And they're more expensive at Asian groceries, or at least at all the ones in my area.
It sounds very much like cow piss when spoken (kah-ru-pee-suu) and the regular version's a milky white color. It has milk and lactic acid in it, is created by lactic acid fermentation and apparently has a flavor sort of like a plain yogurt. A lot of people drink it by watering it down.
In Western markets, it's called Calpico to avoid the obvious joke. You can find it in basically any East Asian supermarket. In Japan, it's normally sold as a concentrate, but there're also pre-diluted ones which is what that seems to be. Sadly, we don't have flavored concentrates in the West.