Does she want any heat in the garage? Does she expect to buy an electric vehicle while living there?

She initially thought she would park her RAV4 in the garage and was interested in a garage door opener but last weekend she parked the car there and found that it was too small so she no longer wants a garage door opener. No heat required in the garage. Electric vehicle would require complete new circuit from the main panel (and main panel replacement) so no provisions for an EV (nor do I expect she will be considering one in this house).

Her house is only 820 sq ft with a total of 9 circuits in the main panel and the breakers total only 190A. The plan is to address the cheap things first until she can save up to address the bigger issues in the house (i.e. knob/tube, Sylvania Main Panel, ancient wiring, imbalanced circuits, only 2 grounded outlets, 1 GFCI, etc.). As her dad it scares the heck out of me but people have been living in it for years and I need to take it one step at a time. Here is the main panel (for reference - I have heard these have had serious issues).

The only answer is to call a licensed electrician.

You could add a "grounding bar" to the box, which would be screwed directly into the metal. Then transfer all the ground wires to that bar. It appears that the existing bar is "floating" (not attached to the box). You could extend the ground to a driven ground rod.

Adding the grounding bar and separating ground from neutral makes sense to me. The existing bar does appear to be isolated with the possible exception of the screw on the right hand side being awful close to the side of the box. Don't get me wrong - we do intend to hire a licensed electrician for the bulk of the work once she has the money saved up. I just want to take care of a few of the safety issues like this one and installing some GFCI outlets if I can sort out the circuit patterns now.

Ouch! Yes those breakers can fall out.

I guess you could just add a ground bar and ground rods.

But I didn't think that a sub-panel was required for a detached garage with a single 15-amp circuit? (I'm sure the "PRO"s here will correct me if I am wrong!) So if you don't like how it is wired couldn't you just remove it?

I thought about eliminating the sub-panel but that seems counter productive. For me this is more about making the place reasonably safe than code compliance. And if properly wired the sub-panel makes a lot of sense. I wouldn't want to see any significant load added as things stand right now but once the main panel and house wiring issues are addressed it would be reasonable to increase the capacity to the garage some time in the future.

Simply pulling the white wires together and isolating from ground sounds like a good stop-gap measure. Thanks