A cupped tire is when your front tire wears unevenly. You can run your hand over the tire and feelm the uneven tread. And they do'nt handle well. I had a Bridgestone 020 do that.
As far as the patching,I had a tire done with a hot patch, the tire has to come off and it is hot patched from the inside. I have a feind that still has a old fasion service station,they don't sell food,but they pump the gas,wash your winshield,check the oil or tires if you want.Have 2 lifts to work and inspect vehicles. And they can fix your tire. Seems like thy're becoming extict,but there are still some around.