Am I allowed to install Snow Leopard on my MBP using someone elses install disc?

Yes, if it's an install disc that was either a boxed copy, or an up-to-date CD, no if it was just the disc that came with the machine unless the model number of the machine is the exact same one.

There are no license keys or otherwise.

You may not be able to install bundled versions of iLife as they are often locked to the machine it was bought from (but even this is get-roundable by showing package contents and using the individual packages rather than the wrapper installer), but the OS is usually fine.

I think the only install media that isn't usable across a number of systems are the Lion USB installers which I believe are tied down at serial number granularity.

Frankly, if you are worried about licensing, just upgrade to Lion for $30.

No.

From your question I understand that you want to use his install disks for your computer. No matter if they came shipped with that computer or he bought it as an upgrade - the Snow Leopard single licence may only be installed on one of your Macs at a time.

Generally, it's possible to use the install disks on another computer. But this depends on the licence you got.

• The install disks shipped with the hardware may only be used with that hardware.
• The Snow Leopard Upgrade single licence may only be use with one computer.
• The Snow Leopard Upgrade family licence may be use with up to five computers.

This is what the Software License Agreement for Firmware Restoration CD 1.9 says:

Section 3: Transfer

You may not rent, lease, lend, sell, redistribute or sublicense the Apple Software. You may, however, make a one-time permanent transfer of all of your license rights to the Apple Software to another party, provided that: (a) the transfer must include all of the Apple Software, including all its component parts, original media, printed materials and this License; (b) you do not retain any copies of the Apple Software, full or partial, including copies stored on a computer or other storage device; and (c) the party receiving the Apple Software reads and agrees to accept the terms and conditions of this License. All components of the Apple Software are provided as part of a bundle and may not be separated from the bundle and distributed as standalone applications.

Version 1.8 of the Agreement is more specific about Restore Copies:

Restore CDs or DVDs that may accompany an Apple hardware bundle, or are otherwise provided by Apple in connection with an Apple hardware bundle, contain a copy of the Apple Software that is to be used for diagnostic and restorative purposes only. These CDs and DVDs may be resold or transferred only as part of the Apple hardware bundle.

Note: There are different versions of this agreement depending on what hardware/software you have.