If I have two Xbox One consoles, but only one Xbox Live Gold account, can I play the same game on the same profile at the same time? Or do I need two profiles + two Xbox Live Gold accounts?
Unfortunately, you cannot play on one Xbox Live on two Xbox One's simultaneously.
You can only sign in to one Xbox One or one Xbox 360 console at a time. If you try to sign in on a second console, you'll be asked whether you want to sign out from the first console. If you respond yes, your account will be immediately signed out of the first Xbox One console.
If you have two xboxs, you can set up one of those as your home xbox. On that particular one, make a new profile. Then, you'll be able to play on that one with the new profile and it will have gold.
Then sign into the other xbox with your main account, and it will work fine.
At least, that's as far as I understand it; I could be wrong as I haven't actually tried this out.