1. Tell me what motherboard you have, and I'll see if I can find the answer regarding the speaker. Not using a speaker will only stop you hearing the POST beep, however it's quite possible that the motherboard has a piezo speaker fitted. They are quite small so you might have one and not spot it.
2. Processor coolers do need a lot of force to fit. I have no experience of socket 775, but the secret is to get sufficient pressute to fit the clip without risking the tool you are using slipping and damaging the motherboard.
3. Again I don't know your processor, but the motherboard manual should tell you. If there's a motherboard connector, then I would expect it to need the power lead.
4. I haven't come across a case that doesn't have the holes for the floppy drive screws, but these days makers don't generally expect floppy drives to be fitted. I would drill the holes in the case if there's somewhere you can do that.