The grey install discs that come with Macs are model-specific and will not work on other models. You can either order replacement discs for your model by calling Apple, or you can buy a retail copy of Snow Leopard.
No, you need to update to Snow Leopard first, so you can gain access to the Mac App Store, where you can download Lion or upgrade to ML. You can't do it for free, if that's what you're wondering.
No. You need Lion for that, as of now. Unless you do a clean install with the available OS X 10.8 Mountain Lion installer, which only developers officially have access to, and others via other means.
No, you need to update to Snow Leopard first, so you can gain access to the Mac App Store, where you can download Lion or upgrade to ML. You can't do it for free, if that's what you're wondering.
But it does say:
"To upgrade your Mac to OS X Lion, you must be running OS X Snow Leopard. If you have OS X v10.5 Leopard, purchase OS X v10.6 Snow Leopard now and install it on your Mac. Then buy OS X Lion as a digital download from the Mac App Store."
Yes, and according to the SLA, you still need Snow Leopard. Whether it works on Leopard or not is another matter.
OS X Lion Software License Agreement
The OS X Lion Software License Agreement allows you to install and use the software for your personal, non-commercial use on all the Macs you own or control that are running Mac OS X Snow Leopard or Snow Leopard Server (a Mac Computer).