It introduces "multa" as an adjective so you can say things like "Many [people from country, i.e. Germans] are [adjective]." Or something along those lines.
Still… that's pretty dumb, don't you think? They could've introduced it by saying "Vi voyaĝas al multaj landoj," or something along those lines.
Well, Australia's had a lot of problems with a rapidly growing rabbit population? This sentence does seem out of place, though.
What do you mean by "uncountable"? Like a mass noun?
mi kredas ke la Esperanta vorto "kuniklo" estas el la antikva greka vorto "kuniklos"