A Dyson sphere around a black hole

Don't black holes suck-in all kinds of stuff all the time, making it a bad place to be for an energy plant?

Black holes don't suck anything in. They just have very strong gravity relative to their size. So just like a space probe would drop into the sun if it got too close, things can get into an inescapable orbit around a black hole. If you can build a Dyson sphere around a star you can build one around a black hole of a similar mass.

They only suck in stuff that gets too close relative to their mass. They aren't magical. If you have a planet and turn it into a black hole with the same mass - anybody on orbit around that planet will continue on their orbits like nothing changed.

For a meteor it makes no difference if gravity is coming from a planet or a black hole of the same mass. The only difference is that once you get very close - the gravity changes much quicker (because black hole is much smaller and denser than a planet) so you will be ripped apart.

> So just like a space probe would drop into the sun if it got too close

The probability for this to happen is actually quite low, ie. it's suprisingly hard to "hit" the sun. The reason is that unless you put the probe on a completely straight path to the sun (which is hard because the sun is so small in terms of its solid angle on the sky), it will have some angular momentum and probably spin around the sun and come right back (more or less).