In theory, yes, a black hole could suck up the sun.
Yes, all black holes 'suck stuff up'.
A black hole near Neptune -- or near any other object in space -- would suck up that planet (or that object). Fortunately, there nearest black hole to our Solar System is several thousand light years away.
Since whit holes only exist mathematically, a black hole could not pull in a white hole.
Yes, it is possible for a black hole to capture another one and "swallow" it.
If it could have we wouldn't be alive NOW.
A black hole will attract you through its gravity - just like any other object will.
Black holes are basically highly compressed massive (has lots of mass) parts of space. The large amount of mass warps the space time around the black hole which causes intense gravity that suck everything in.
A black hole will suck you up in to a long piece. You will be stretch like spaghetti then be crushed.
Fortunately, no.
A black hole doesn't literally suck. A black hole pulls things closer to it. And it does this the same way that we stay on the earth--- gravity. A singularity, a point with mass but no height, width or length is at the center of every black hole. This singularity is what has the gravitational strength to pull everything, even light, towards it. It does it all with an unfathomably strong gravitational pull.
It is scientifically impossible to have a black hole in any parts of the Earth. If there was one, means that the tiny black hole would suck up everything, even time and even the moon.