Install snowleopard over lion on a another partion

Assuming your MacBook Pro supports Snow Leopard and you have an SL DVD, you would first need to back up your system. Next, use Disk Utilities to create a 2nd volume (partition) for Snow Leopard (Mac OS Extended (Journaled)). Last, boot from your SL DVD and install SL to the new volume.

How old is your Macbook Pro and what OS came preinstalled?

What OS was installed when you purchased you Macbook Pro? It's possible the beeping noise when booting from the SL DVD is because your Macbook Pro hardware will not support SL.

I don't know. You can search the internet. You might be able to use a VM, but I don't know for sure.

I don't know. I don't run a VM. Maybe someone else with VM experience can help you.