Are there any general rules about how large, how many and where mounting holes and the like can be drilled in a frame and other critical areas?
Heavy duty truck frames must not be drilled in the flange, only the web, although I've seen exceptions. The flange is the part that does most of the work. Car frames don't normally get stressed as hard so they have holes in the flanges. If you are worried about adding holes, do so only in the web, as HRP shows.
The flange is the horizontal part of the frame that resists side loading and carries weight, while the web is the vertical part that primarily carries weight. A frame section supported at each end loaded in the middle is in compression at the top and in tension at the bottom,. There is a neutral axis where there is no stress in the frame. Holes and welding at the neutral axis will not significantly affect frame strength. Regarding truck frames, holes and welding near the hardened flanges can cause frame failure. Chassis manufacturers restrict the size and location of holes, and most also restrict welding on the frames. In heavy trucks/semi tractors the flanges are heat treated, whereas the web is not, so any modification of the brittle heat-treated areas, or areas close to it, can result in cracking. The car frames that most HAMB'ers work with have no heat treating. Nonetheless, it's not a good idea to drill a hole anywhere close to the edge of a flange, nor to leave any abrupt inside corners where modifications/welding have been done.
If you bell the holes like aircraft frames you will add some strength over flush holes. Common sense in use of holes, size and centres.