Some parts of this are quite easy, others are more challenging. Generally speaking, the approach I'd recommend is creating a new extension that has Money and Best Answer as dependencies (listed in the require section of composer.json). Possibly this might need to be a fork of FoF Gamification.
Omnivorous Connecting Money and FoF Best Answer: New listener in Money for when a post gets the best answer, the poster should get all the points given to the opening post in their money balance.
You could have event listeners for the events dispatched in https://github.com/FriendsOfFlarum/best-answer/tree/master/src/Events, this is relatively easy.
Omnivorous Connecting Gamification and FoF Merge Discussions: When two duplicate OPs are merged, the points given to them should be added up.
Similarly, you could add an event listener for https://github.com/FriendsOfFlarum/merge-discussions/tree/master/src/Events. This is also pretty easy.
Omnivorous Overriding FoF Gamification's behavior: Instead of upvotes or downvotes, I want members to only be able to transfer as many votes to a discussion as how much money they have in their Money balance.
This one is a lot harder: there's a PostWasVoted event, but I'm assuming you'd want a UI for users to select how much of a bounty they're putting on a post. Also, IIRC, gamification uses its own points system, and you'd want to use Money. I think the easiest approach here might be forking FoF/gamification and rewriting the internals to work as a bounty system based on Money. That extension would also contain listeners for the events I mentioned above.
