Can a stellar mass black hole swallow Earth? In the Astronomy magazine I read that the stellar mass black holes are only the size of Rhode Island. Can they swallow Earth?
There's a fairly common misconception in this question that black holes "suck everything in".   They do - at distances close to their event horizon but as noted, the event horizon's diameter is about the distance across rhode island (different masses have different sizes), but many stellar mass black holes would fit inside the border of rhode island.  Virtually all of them would fit inside pennsylvania for example.   They're tiny.    I'd rate my chances of survival as much higher in a space-ship 1 million miles from a stellar mass black hole than in a space-ship 1 million miles from our Sun.

At normal planetary distances, a planet would just orbit a black hole and likely maintain a stable orbit for billions of years.   Gravitationally, they're no different than a star at those distances.  The orbital mechanics is based on mass and a stellar mass black hole has stellar mass.   What makes it different is it's shrunk inside it's schwarzchild radius, so compared to stars, it's incredibly small and very dense.   The "weird stuff" only happens at very close distances - basically at distances you can't reach around a star because you'd be inside the star.

So . . . what would happen if you put the Earth next to a black hole.

I'm not sure why you'd want to do that, but the Earth would begin to break apart form tidal forces before it got that close.  The gravity would be stronger on the near side than the far side and the Earth would stretch.  This is called spagettification.

If you theoretically made a black hole just appear near the Earth then it would begin to eat the Earth.   Think of a black hole as a drain, a drain some 20-30 miles across, and think of the Earth as a liquid trying to get down that drain.   It's a lot of material squeezing into a comparatively tiny space and in the process the Earth material would get very hot, and likely form into an accretion disk trying to get inside the black hole and the formation of the accretion disk would eject two cosmic jets along the axes.   Black holes are sloppy eaters.

I couldn't tell you the precise amount of Earth that would be absorbed if they were placed right next to each other, but that's also an impossible scenario.   Everything in space is moving and gravity guarantees that if the Earth did meet or closely orbit a stellar mass black hole, that it would be moving enormously fast.   

Earth could in theory, but extremely unlikely, either orbit a black hole or collide with one, or pass very close to one, close enough to break apart.  Each scenario would have a different outcome with a different percentage of Earth falling into the black hole.

I don't feel like going through each scenario individually, but the short answer is that the Earth would get quickly ripped apart and some of it, but not all, would fall into the black hole.  Some would be ejected as high speed charged particles.   The matter spiralling in would create a very strong magnetic field and because protons and electrons are charged, much of the matter wouldn't entirely follow the gravitational forces.  Some would get shot out as jets of charged particles.  

That's a rough answer anyway.