1. 7d and 500mm f/4 is 800mm equivalent and f/5.6 equivalent like DOF capabilities and rendering the fore/backgorund.
2. 5d iii and 500+1.4 is 700mm f/5.6 mm lens
Nearly - the 1.6x crop makes a 500/4 equivalent to a 800/6.4
lens vs a 700/5.6 on FF with a 1.4x TC
So in reality, the 800/5.6 behaves much like a 1280/9 on crop, vs an 1120/8 on FF and 1.4x TC.
I'd also argue that the supposed 7D2's AF system would be focusing at f5.6, vs the 5D3 at f8 - that should be an advantage, plus the FPS is nearly doubled. As stated, there's more than the theoretical 1.3 stops difference in S/N between the 5D3 and 7D1, so the gains of the faster lens are more than lost. But this is the unknown quantity of the 7D2 - who knows what it's S/N is?
You do not want 800 for crop. Your subject will be to far away and the air between the lens and the subject will blow your IQ. Believe me. Even 600 is to long for crop sensor.
Depends upon what size object you're focusing on. If it's as small as the lens can frame, you're only 6m away from the object - no issues there with the amount of air. If the humidity, pollution and heat haze levels are favourable, 100m could be perfectly fine. And other times getting closer simply isn't an option, so starting off with a competent lens/body can't hurt, even if the conditions aren't the best.