We'll respond shortly.
"What's the latest and greatest server-side image processing library people are using?"
Most people quickly agreed that ImageMagick was the way to go.
"Are there good libraries for data analysis similar to NumPy in Python but for Ruby?"
While there may not be many Ruby libraries that directly comparable to NumPy, there are a fair number of packages to do related work. For instance, you can utilize RSRuby which is a bridge between the R statistical language and Ruby. GnuPlot is another Ruby library that allows both data processing and plotting of graph data.
RSRuby – R / Ruby binding
GnuPlot – Data processing and Plotting