How to set up 2 Sonos Amp in 1 Sonos account to play different music?

Each Amp will be a different Sonos ‘room’, you just tell each room to play its own music stream, or you can group the two ‘rooms’ together to play the same stream. 

Oh, the other question…the Sonos system runs on the device, it is not running through the controller. Think of the controller as just a remote control, you can have up to 32 remotes associated with your Sonos. 
 

Although you’ll be able to control them from your pc, you’ll need to install them onto your network using a phone app - IOS or Android versions of the app are available. 

Thank you for your feedback,

If so, I will need 2 music streaming accounts for 2 Amps, right?

I currently have a Spotify account. If I operate in the above way, can I use another Spotify account or do I need to register for another music streaming?

I will take note of this, thank you very much

Each streaming service has their own limits as to how many simultaneous streams they’ll support on Sonos (and elsewhere). You may want to ask Spotify to see what their policies are, and take a look at the FAQ on the Sonos website. You can, however, if you choose, set up multiple accounts per service.

Not that I use it very often, but with Spotify you can use more than one stream on Sonos (via the Sonos app) on different Sonos devices. Just tried it on my system to verify.