I thought the instant communication was cool. Just 50 years ago the idea that we could have instant global communication was science fiction. Who knows what they'll have in 250 years' time? Surely all you need is enough bandwidth and a ton of booster relays dotted around Federation space. NX-01 Enterprise laid the first few and kept real-time communication with Earth. And they passed Kronos in episode one.
As for how they got everywhere so fast - speed of plot. In Voyager, warp speed is incredibly slow. In every other Trek, they get where they need to go in the space of a scene break - in DS9's case, usually via tiny Runabout.