This is my sons car so I have not been driving it: Power steering fluid under car just under power steering fluid reservoir area. Reservoir fluid level is below bottom fill line. Filled it to top fill line. Started car and loud sounds from power steering as I turned steering wheel through range a few times but better after that. But fluid foamed up and leaking around cap. No hose leaks. Symptom of what?
Foam is usually a sign there is air in the system, whether the air is getting sucked in through the cap vent due to a lack of fluid or through where the leak is at. Either way, you've got a leak in your system. You need to figure out where that's at and then get it fixed. Once fixed, you had the right idea about turning lock to lock to purge the system. What I didn't see you mention is that you did this with the front end up off the ground. When purging, not only does it work faster to do it with the front wheels off the ground, it's also easier on components. After you've purged, it should be in good shape, I'd think.