The label on your hydrometer should tell you what temperature it was calibrated at, look and see because they are not all calibrated at 60F. Measure distilled water at that temperature and it should read 1.000. Tap water will be pretty close as well. If it is off make note of the difference and you will either add or subtract that amount every time you take a reading.
Your hydrometer reading then needs to be temperature corrected depending on the temperature of the wort/beer you are testing
For your thermometer, fill a glass of ice water and it should read 32F, then boil water and depending on location it should read 212F. Any differences should be noted and readings get adjusted the same. If you can accurately get a reading at 150-152F, that would be ideal as well since that is a standard mash temp.
If you mashed low then your wort was more fermentable and will generate a lower FG. Conversely if you mash high then you get a less fermentable wort and higher FG.
If you have reached 1.004 and it continues to drop then it is possible you have an infection that is chewing through the less fermentable sugars, if it is stable then it shouldn't be an issue
So if its stable at 1.004, does that mean ill have a lot more alcohol content than planned?