I’m glad that your Dad already replaced the fuel filter, as that would normally be something I would recommend, based on the symptoms. Where Dad is off base is in his belief that “the computer is freaking out” because the engine was run low on oil at some point. Trust me–the computer knows nothing about how low the oil level may have gotten in this engine–but the bearings may have intimate knowledge of running the car low on oil.
In other words, even though being run low on oil is not a cause of the symptoms that you are talking about, the engine may have been damaged by a low oil situation. However, with 230k miles on the odometer, I wouldn’t worry too much about the engine at this point. If it begins losing oil pressure due to worn bearings, or if it begins burning way too much oil, you could just have a junkyard engine installed.
But, to return to your current problem, there could well be multiple causes, as stalling while driving and having a hard time with a hot restart are probably not related. For the stalling, you might want to try cleaning the Mass Air Flow sensor (MAF). The problem with hot restarts could be the result of a leaking fuel injector. A bad fuel pressure regulator could be related to both issues, however.
Also, while you are under the hood, you might as well replace the spark plugs and plug wires if they have not been changed in the past 3 years or so.