When you get the hand wheel loose, take it off and grease parts. It will not get stuck like that again (...well. in the next 6 years or so) I'm not sure with the 503, but it might have oil points under the lid; if so tilt the machine to the right to persuade the oil to seep all the way out to the stop motions screw (place thick book or something under the left side). These old machine can take some time to get tuned up; in the sense that when you initially clean and oil them you free them up, and when you start using them you get to tend to all the minor things turning up along the way. Stick with a machine as see it through, and some of these machines are built to service you for life.
Your Touch & Sew motor might need cleaning and greasing, and there might be thread bits, or something that needs to be cleaned out (thread wound around a hand wheel will gradually stop a machine, can be invisible until you take it off). Inspect gears, plastic can crack, if just a bit they usually still run, just very noisily.