Goa in Monsoons is a very different experience. If you are planning for it, go ahead.
Best time to visit when the sun isn't harsh unlike summers and you will get to witness the greenest of greens.
I visited Goa in March and it was burning hot so definitely not recommended. Also, cafes and clubs are open as before but with necessary precautions.
Yes Goa is open for tourists . If you travel responsibly with all safety precautions , it shouldn't be a problem .
Some popular cafes and restaurants are open like Artjuna, Baba Au Rhum , Titlie , Brittos etc . However owing to the rains , the beach wouldn't be accessible at all times , so plan accordingly .