This started as a comment but grew into an answer.
Summary: I'd try to characterise that IC in the current application, possibly with advice from Allegro. It's a beautiful solution and you'd be hard put to better it if you can work out how to live with the bandwidth issue. [I have no relationship with Allegro apart from having been an occasional very small scale satisfied customer].
People "would be well advised" to look at the Allegro ACS758 datasheet
before commenting.
Allegro are very competent and this is an extremely real; solution. In practice it is liable to be a very serious solution to have to compete against with things like PCB track drop. It's calibrated [tm] \$ 100 \mu \Omega \$ current path and isolated sensing, factory trimmed parameters and formally specified rise times are not going to be trivially matched by 'bits of copper track' and an op amp. Better solutions may exist, but they are not one liners - unless the one line is a part number.
Here is Allegros range of High current sensors
Note that the ACS758 is at the top of the range both for current and for bandwidth.
The datasheet specifies bandwidth as being \$ \frac {1}{3 \times T_{rise}} \$ and \$T_{rise}\$ is typical. Performance is in the order of right to rather marginal. Given the otherwise superb nature of the part I'd take a very close look at how the device behaves at target frequency. There will certainly be "roll off" but how much. Is something like a single pole, which can be happily used an octave or even two above notional cutoff, or is it an 8-pole-boxcar-go-away-use-something-else response? I'd suspect more the former than the latter.
If I was doing this and wanted unlimited freedom of manouver I would indeed start with a resistive voltage drop solution. But I'd not be surprise if the chase was long and hard. For any sort of accuracy across temperature I'd probably want to use an add in resistive shunt, and something of the magnitude of Allegros \$ 100 \mu \Omega\$ shunt would seem about right. (\$50A \times 100 \mu \Omega = 5 mV\$ drop. \$(50A)^2 \times 100 \mu \Omega = 250 mW \$ loss. Note that a \$1 m \Omega \$ shunt takes 2.5W and a \$ 1 \Omega \$ shunt takes \$25W\$. Even \$2.5W\$ may be considered "intrusive" depending on the system Voltage.
\$5 mV\$ full scale drop = \$20 \mu V\$ per bit at 8 bits. Not "hard", but offset voltages become important. But with devices PWMing 50A nearby, using an off theshelf solution that had dealt with such issues looks more attractive than sometimes. At $US7 in 1's and half that in 1000's the ACS758 looks like a good start.
That is correct.
A capacitor is needed because such ADC are SAR and as such the switching can cause an upset to the part in question.
Typically a SAR type ADC requires any input pin capacitance to be a minimum of 10x the Cia to ensure that when it switches the actual voltage on the input pin does not droop (before said capacitance can be trickle charged from any sensor).
4.7nF satisfies this and is a typical value I would use when connecting Allegro devices directly to an ADC. The only times I consider placing a buffer between the Allegro and an ADC is if I require a larger capacitance (usually due to filter time constant concerns)
Not to sure about explicitly placing an Rl in parallel with the sensor, in series with the output to produce an RC filter may be of more benefit
Once piece of advice. The benefit of these devices over others is their ratiometric gain w.r.t. supply voltage. Ensure such a device is as physically close to the ADC as possible to ensure the ADC and the HES share the same rail so the ratiometric nature of the ADC & HES can be taken advantage of (by same rail I don't mean 5V powerplane on a 1m x 1m PCB... I mean their power pins as close as a via and decent local tracing will allow)
Best Answer
On most op-amps you cannot properly use an input signal that is below the - supply pin. You might try to bias the sensor output to 2.5v (with equal pull up and pull down resistors on the sensor's output).
Alternately, to set up a true level shifting circuit see these examples that use hall effect sensors:
http://www.next.gr/sens-detectors/hall-effect/current-monitor-l13368.html
http://www.instructables.com/id/How-to-Measure-AC-Current-using-Hall-Effect-Sensor/