Yep, "is the cider doing the right thing" can be a bit of a worry. We have all been down that path.
As RPH Guy said, the hydrometer measures the SG of your juice. Some hydrometers have a potential alcohol scale which shows what might happen if you ferment down to 1.000, but this alcohol scale should track the SG as it changes when fermenting consumes the sugar and the hydrometer progressively floats lower.
It does sound as though it is all working the way it should.
Your two cups of sugar might be a bit of an overkill. My notes of "interesting information" suggest that a cup of sugar in a litre of water results in a SG of around 1.075, so your two cups in a gallon will possibly add 0.030 to the juice which was probably 1.050-1.060 to start. Boom!!!
A rough measure of ABV is 1.31 x (starting SG-finishing SG). In your case the sugar will likely push it over 10% ABV which is getting into wine territory.
If your cider has been bubbling away for three weeks, it is probably down around the 1.020 level, finished its turbulent primary fermentation and ready to be racked off the lees into another carboy. Do this with an airlock in place and top up with AJ to minimise the airspace. Then leave it in secondary until the bubbling has finished and the SG is down around 1.000.
At this stage you should have a somewhat tart, still cider that will taste "alcoholly" as the sugars have been converted to alcohol and CO2. If you want carbonated cider, add 1-2 teaspoons of sugar per litre and bottle with sealed caps. If you want to get a bit more scientific, the alternative is to add sugar or AJ to bring the SG up from its finished gravity (usually1.000) by somewhere between 1.003 and 1.005. The extra sugar will be consumed and produce CO2 which is absorbed into the cider and released as fizz when the bottle is opened.
As in the previous post, make sure that your technique for reading the hydrometer is good. I wouldn't fuss too much about the calibration as you are looking for relative changes rather than absolute changes. Do you really care if the potential ABV is 9.4% or 9.8% as the rocket fuel effect will be much the same.
If you are going to continue down the cider path, invest in Claude Jolicoeur's "The New Cidermaker's Handbook" and also read the stickies at the top of this page. It will tell you almost everything you need to know. Good luck!
