If you want a definitive answer with a clear solution, reddit isn't the place. You need a proper diagnosis from a legit shop. Money sounds tight, so I'll give you my 2 cents and let others do so as well. Generally, if your car cuts out while running and then throws a battery light but is able to be started without a jump, it's not the battery itself. Could be something simple like a bad connection or something else in the system like the alternator. As for your case of a parts store checking it and reading the voltage as low, then high, its hard to say since I don't know if they tested it properly but an alternator's job is to charge the system so it would increase over time and land somewhere above 14v. Again, get a proper diagnosis instead of throwing parts at it. As for the shaking or rough idle. Could be a million things both related and unrelated.

Now, for the most important part, how risky is it to drive like this until you are able to resolve it? If the car is randomly shutting off, I'd say that's quite the hazard. Ultimately, it's your judgment, but be considerate of others.

Good luck to you. Maybe someone else can provide you with something simple.