I have built a golf simulator in my garage that we can use as a media room.

Our current projector has a small speaker so we currently are using that with a roku stick for movies/shows.

My question is can I take my gaming computer, connect to the projector as a extended desktop, play a movie from my computer and finally connect some Bluetooth speakers to my laptop for louder audio?

Currently when we play from our laptop to the projector, the sound comes from the projector and not sure if I can change that or not.

Yes, you can pair your laptop to the Bluetooth speakers, then redirect all the laptop's sound to that. Not sure if there will be a significant lag or not.