Can we simulate a black hole on earth

Similar to the ones in our solar system but on a smaller scale (micro black hole)?

Not necessary. Tiny black holes are all around (and in) us.

A proton will decay only extremely rarely, but there are so vastly many of them that a proton will decay within your own body several times a second. When a proton decays, a tiny black hole is formed. It is so small that it evaporates in an unimaginably small amount of time.

If you mean a black hole with a diameter of about the same as a hydrogen atom as in the movie, "The Krone Experiment" then no, we can't do that. (Also, there are none of that size or larger in our solar system. Although tiny, that fictional black hole had the mass of a small mountain.)
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At the Large Hadron Collider (LHC) scientists are hoping to do just that. To make an artificial black hole requires immense energy, and the LHC may just be able to come up with enough.

Some misinformed and/or scientifically ignorant people have been running around blathering about this LHC black hole and how it will destroy the world. Dumb! The LHC black hole would be, as you mention, a micro black hole and last for far less than a nanosecond.

I read once in a Science illustrated or Popular Science magazine that there is a theory that we can use the power of Hawking Radiation (the type of radiation given off by black holes) to power space ships by creating a small black hole in a pan-like holder where the rockets would normally be.

There are none in our solar system, as far as I know

re. simulations, a few experiments have been described as mimicing a black hole

I think the closest thing would probably be when a nuclear explosion occurs it blows all air away and creates a vacuum.

They are actually working on that problem at the Hedron facility in Europe, if it works Europe will be the first to go.