Re: Slowing down, reversing, etc. is done by firing in the opposite direction.
I know.
My point - does it take 50% of the fuel and 50% of the travel time to slow down enough to go into orbit around something?
The ion drives are used for navigation, not for getting into orbit in the first place.
There is study into using ion propulsion for interplanetary and similar long distance. You are partly correct, the amount of energy used to accellerate is the same as the energy to decel (in open space), so if the mission used 50% to speed up, then 50% to slow down. Or 20-20, 31-31, or whatever "equal" amount.
Getting into orbit around an object is a little more complicated, but the "same amount" approximation is good enough.