I have the the same setup that you are talking about in my own home. Except I have a couple of old routers that I converted into switches, though I wish they were Gigabit and not 10/100...
1) A regular ethernet cable work just fine. Just be sure it's Cat 5e. Cat 6 can be used though it's a bit overkill for home use but it doesn't hurt!
2) Getting an unmanged switch, 5 port or 8 port (your choice) from Netgear. Run 1 cable to the switch from the router. The switch will take care of everything.
3) If you set up Windows Server 2012 correctly and Anywhere Access, you'll be able to view, download, and add files to and from the server. It just take's time to setup. A lot of time. (I'm running Windows Server 2012 Essentials R2 and it saves me a few steps if you're using the Standard) [since you're using 2012, do this command in an elevated (administrator) on your client computers 'reg add "HKLM\SOFTWARE\Microsoft\Windows Server\ClientDeployment" /v SkipDomainJoin /t REG_DWORD /d 1' if you don't want your computers to join a domain since it forces when running the connector]
4) That depends on how big your house is and how big of a radius of your router will emit. If you think that you'll need a wireless repeater, buy one.
5) Like I mentioned in 2, unmanged.
6) Sharing folders/drives on the server and then mapping them on Windows machines will do perfectly fine.
Source: Personal experience, Microsoft and networking major, Google