There are canon (or at least common headcanon) explanations for these two things.

The ESB one has been debated for years. But basically, the Falcon has a secondary, albeit extraordinarily slow, backup hyperdrive. It’s like a spare tire for space travel. This also explains how the Empire and Boba Fett got there before they did once they knew where they were going.

As for why everyone can see the destruction of Hosnian Prime… it’s definitely a hand-wavy explanation but this is what Wookiepedia says.

When the Starkiller Base superweapon released the quintessence [dark energy] it had collected within its core, it was transformed into phantom energy [another state of dark energy], which would follow the line of egress that had been provided by the weapon’s technicians according to planetary rotation, inclination, etc, through a hole in “sub-hyperspace”, until it was intercepted by an object of sufficient mass. When the beam of phantom energy interacted with a planet, it ignited its core, creating a pocket nova. Large amounts of phantom energy could create temporary rips in sub-hyperspace, which allowed the Hosnian Catacylsm in 34 ABY to become visible from across the galaxy as it happened.

So basically, since the weapon made light/energy travel faster than lightspeed itself, it created a disruption in space-time, which made it so the light from the destruction was visible at hyper-light speeds across the galaxy. So not only could the people on Takodana see it, but so could everyone else if they were facing the right direction. I know in the video game Battlefront 2, the characters can see the Hosnian destruction from another planet called Vardos.

But the better answer is that it’s just Star Wars, the same galaxy where starships fly like there is air friction, where you can hear sound in space, and giant worms live in asteroids. Did I forget to mention the space wizards with laser swords?