You may have more than one issue. 1st did this just start or was it after the car sat for some time? Good chance the carb needs a rebuild, especially if you have been running ethanol gas. You could have a stuck float, a damaged needle valve, a blown power valve etc. all would cause flooding conditions.
I would also suggest you post this over in the Vintage Mustang Forum. There are some real experts on the 60s engines there.
How old is the oil? Over time it is normal to get dark, but if it happens quickly it could mean the engine is ready for a rebuild and the rings are leaking. You need to start with some basic diagnostics.
1. Vacuum check
2. Compression Check
These will help identify the condition of the engine. If it checks out OK, then you need to look at rebuilding the carb and doing a tune up.