What do the BlendJet charging light colors actually mean?

If I leave it plugged in after the ring turns solid blue will that hurt the battery?

No it will not but lithium battery degrade over time when they are at 100% most of the time. It may not matter with the BlendJet but over the lifespan of the product it could degrade more faster.
 
Mine started blinking purple and red around the year mark and would only last one blend before it ran out of charge. The support agent basically told me it was out of warranty and offered me 20% off a new one. I ended up purchasing a different brand.