By looking at the glowplug, what color it is, if it is wet or not etc, there are some tell take signs about what your engine might be doing. Ultimately, for the cost vs guessing, I would just install a brand new plug and be done with the questions. They aren't so expensive that it's worth...
Agreed. You may also have an issue where the glow plug temp is too high or low for the ambient temp you are running in. Its fairly common where we are in season for drastic temp changes as the seasons are changing.
Def let us know how everything goes at the hobby shop too. Keep in mind that the setting they use there may all be different than what you actually need. My guess is that your carb was set while it was warm. Between the car ride to the store as well as the temp in the store itself... That is DEF...
Be careful with heating when you get low like that. Just be careful you are only heating metal components. Stay away from the carb as there are pieces of rubber in there that can be hurt from excessive heat.