If time really is a dimension then what does it look like? Long branching strings of everything from beginning to end?
Yes
Would not that affect the gravity behavior of systems if there was {mass\energy} distributed along the time axis?
Yes
I would think that would provide a means to correlate minutes to miles ...
Yes
the only problem I see is that it makes the universe pretty deterministic, already written into the future yet to be revealed.
Yes, it does...
Now, just jump into your time-machine, race back 100 years, and it will be RAZDs General Theory of Relativity