Question: Is it possible to "pump" a powder the same way liquids can be pumped?

If so, what are the challenges? If not, what are some alternatives?

Answer: 
I believe it's termed "injecting" not "pumping" but yes, it's certainly possible.

Coal fired electric power plants grind the coal to a very fine dust and then blow the dust into the central burner.

[This particular article](http://www.netl.doe.gov/File%20Library/Research/Coal/major%20demonstrations/cctdp/Round3/bethstl.pdf) is a summary of some DOE research for a Blast Furnace Granulated Coal Injection System Demonstration Project.

And [this article](http://www.nfpa.org/~/media/Files/Research/Research%20Foundation/foundation%20proceedings/david_snell.pdf) discusses some of the hazards from a National Fire Protection Association perspective. Coal dust having the particular dangerous property of being explosive and all that...

As far as specifics regarding danger, I suspect it will vary depending upon the material(s) involved in the powder.
In food process you can "pump" powder with vacuum, sugar works very well, and some other products need sometimes some technical adjustment (pression or open/close cycles valves) .
But water in the pipes is ban and last point it's only for small quantities and short distance 20meters max i think.