Does anyone know the official name of the part inside of the red box on the attached diagram? Two of the bolts that hold this on came loose and fell off, so I'd like to replace them. Any help is appreciated!
Although I don't know the official name of that chassis piece, the easiest way to replace the missing bolts is to remove the other two bolts and the bracket, then take one of the bolts to your local hardware store to obtain two matching metric-sized bolts. Good luck.
You might be interested in the G7 plate since you will be underneath working on that part: G7 Performance Stiffening Plate 04-09 Toyota Prius | eBay
Yes, this is the factory stiffening plate. Some people replace it with a wider/thicker one of machined aluminum for improved ride/handling. The new plate comes with its own attachment bolts, so if you wanted to replace your plate you wouldn't need to find replacements for the old bolts. Or you could find someone who replaced theirs and see if they would send you their old bolts if they still had them around. I don't know whether I can still find mine or not.