for no.1, i'm not sure but i don't think it will cause any problem.
for n0.2, you can add some washer between the bolt and the back-plate, it should be able to hold the port in place, but if your i/o shield is just a thin piece of metal then it won't feel secure when insert the gamepad for sure.

2. No you are not supposed to screw connectors that are not part of the motherboard on the I/O shield. You can of course "put" it there as it physically fits, but it'll never be sturdy enough to plug and unplug joysticks. You will be putting force on the I/O shield itself and most of them bend easily, that space is intended for the gameport of an on-board sound card. AT cases had places on the case where you could do that, some ATX cases that support AT motherboard had them too, but later purely ATX cases don't.

Splitting the PC speaker signal from the motherboard header to two outputs will work, but the volume will be lower on both outputs. Not sure how low though.

But I would not go with this setup as it would drive me crazy to hear the beeps simultanesously from the PC speaker in addition to the speakers from the sound card.
Also, I never liked the sound of PC speaker square waves routed through a sound card. It hurt my ears, and adds things like bass/treble boost to the signal... bleh.

I bought and used the y-cables, and nothing caught fire, so great success, I guess.

I agree that listening to PC speaker output through both the case speaker and desk speakers would be maddening, but I'd only be using it for capture. The desk speakers would be muted during play.