Never tie anything to green/ground, that conductor (although it doesn't look like it's hooked up at all to your furnace which is.......ugh) should never be used to carry any current, even from a small relay coil. If your last picture is the cord coming from the wall/outlet in the bottom of that box, black from the wall cord "should" be hot and white "should" be neutral. In your last pic, purple is tied to hot/line from the wall and the other black(furnace/blower wire?) is tied to *white* from the wall, which is, or should be, neutral. Looking at your first pictures, it looks like you tied the purple wire onto the "load" side of the fan control - if this is the same purple wire in each location, it most likely was originally on the "line" side of the fan control/limit switch and has been reversed by mistake. Without a schematic or understanding where every wire on that furnace goes, due to the odd color schemes, tying black with white/neutral/etc you are treading on confusing and possibly dangerous ground until you have understood/mapped out the complete set of circuits you are dealing with and know what all the wire colors should be going to, which ones are hot and neutral, etc. You should really have a multi-meter to verify your hot/neutral from the wall, a schematic (factory or diy drawing from tracing out all the wiring), and a complete understanding of the wiring before you go further.