What is the proper way to set the offset and sensitivity parameters for Allegro A1362 so MSP430 properly digitizes them?
The preferred way to set up the Hall Sensor for initial experimentation would be to acquire the evaluation board, and then follow the instructions to use its software for calibration and configuration.

If that is not an option, similar results can be achieved manually, albeit with a bit more effort and some guesswork / empirical data. This is how it goes:

Required parameters:


Expected magnetic field strength - active range expected? 

Intrinsic, earth's magnetic field at surface = 300 to 600 milliGauss
Small toy magnet or fridge magnet = 30 to 150 Gauss

Expected rate of change of field: How many cycles per second?
Vcc of MSP430? 

MSP430 digitizes from 0 to Vcc, and can tolerate up to Vcc+0.30 Volts
Permissible Vcc is up to 3.6 Volts

Expected / desired full-scale range from Hall Sensor (assuming ADC10 of MSP430 is being used)?

Both upper and lower references can be changed from default GND and Vcc, to external reference voltages, 0 to 1.2 Volts as lower reference, and 1.4 to Vcc as higher
Internal voltages references of 1.5 Volts and 2.5 Volts are also available, to use as the full-scale limits.



Once the above parameters are determined, a suggested way to proceed would be:


Program quiescent voltage to around midway between the MSP430 ADC10 reference values you select
Determine actual sensitivity of your sensor using the magnet of choice, and a good voltmeter: The manufacturing tolerance range is pretty high. For instance, if using strong fridge magnets, the highest sensitivity range, 4.5 - 16 mV/G, could give a maximum of 4.8 Volts full-scale North-to-South, way more than the MSP430 can handle.
Program sensitivity based on above tests, don't use the maximum sensitivity mode of the part.
Don't count on built-in clamping of the device, use an external clamping arrangement if at risk of exceeding MSP430's Vcc+0.30 Volts.
Opt for ADC reference voltages in between the rail voltages instead of full 0 to Vcc, that way there is margin for error in case the sensor overshoots expected full-scale voltage, e.g. if a mobile phone rings nearby.
Use a capacitor on the bandwidth FILTER pin such that your bandwidth is limited to perhaps 10 times the expected cycles per second mentioned above - otherwise the output gets too jittery, even if a person with coins in their pockets walks by.


That's what I can recall off the top of my head, but if additional details are required, please edit the question accordingly.