Am I able to stream PS3 games to the PC and then to twitch with galaxy 2.0?

no, you want psnow

All this does with PS3 games is to list them as owned in your library and import trophies, no way to actually interact with the PS3 from the Galaxy client.

Unless I'm missing something that they've added in the last update, GOG doesn't scan your PS3 games or trophies.
As far as I can tell, it's not scanning physically owned PS4 games either, only digitally owned PS4 games, as least for me.
The only way to get your PS3 games to show up in your library is to add them manually, and even then it won't scan for trophies.

Oh, yeah, you're right about it only picking up digital games, not physical games you've gotten trophies for, and I guess the ones I got trophies listed for where the games I own both on Vita and PS3, so maybe it's just the Vita trophies it's listing.