Answer for Will a coconut oil coffee break your fast?

The general rule of thumb is anything less than 50 total calories won’t break your fast. So 1/2 TBS coconut oil is about 59 calories and add the walnut milk I would say you are breaking your fast. I would do it without the coconut oil. 
It depends some on the type and intensity of the workout and what your goals are.  In keto-adapted athletes, ketones are burned in place of BCAA.  Your muscles will actual go though a change where they reject insulin (and as a result glucose) because they PREFER to burn ketones over glucose.  So your muscle energy comes from ketones, not glucose.
If it is an intense heavy lifting session where a lot of muscle repair is required, then a meal after the workout would be beneficial for muscle repair. 🙂