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.
While pumping powders as a mix with swiftly moving gas is viable, one of frequently used alternatives for both powders and granular materials is [Archimedes' Screw](http://en.wikipedia.org/wiki/Archimedes%27_screw).

![enter image description here](https://i.stack.imgur.com/KE01J.gif)

Essentially, a helix in a diagonal pipe making the material "pour/roll" upwards the curve, allowing lifting it a long distance. This solution is frequently used in farming equipment for transporting grain or granulates. While it doesn't provide "pressure" for moving it through inert pipes, a "pipeline" of such screws can go a long way, and while it restricts transport angle, it provides a viable alternative especially for heavier materials where extreme air flows would be required to move them.