Icon fonts require all shapes to be filled-in paths; borders/strokes are not supported. I would Convert to Outlines on any of your borders in Sketch, and try to combine all of the layers for each icon into a single combined shape. That should produce more reliable results, when making glyphs in a font.
Yes. Roughly 2/3 of the course will be applicable whether you’re using Sketch or Illustrator. There’s so much to cover about SVG and how it works, and even the Sketch workflows will often be similar to what you need to do in Illustrator.