A confusion about error components in a data acquisition system
My question is: Are the gain and offset errors in the data-sheet fixed values or are they maximum values and also statistical or indicate a range?


As pointed out in the other answer, the actual error varies from device to device, and when the temperature of the device changes, and maybe in response to other effects like if the power supply varies, etc.


  For example, if data sheet says offset error is x, and my mean reading is A; should then I correct my reading as A-x ? or x is not constant?


The datasheet normally says the maximum error is \$x\$. Then the actual error could vary between \$-x\$ and \$x\$. They might mean this as an absolute limit, or they might mean this as something like a 3-\$\sigma\$ or 6-\$\sigma\$ limit.

If the number was an exact statement of the error, constant across all devices and temperatures, etc, the device manufacturer would have been able to adjust the device to eliminate that error and sold you a device with 0 error instead of \$x\$.


  Or if it is not fixed should I measure offset before each measurement?


Measuring offset might help you to reduce the error in your measurement. This would be a form of calibration.

But remember not all errors are offsets. It's also possible there's an error term that's proportional to the measured value (a gain error). 

If you have some "golden" target to measure, you might even be able to calibrate out the gain error as well as the offset. 

That would likely reduce your measurement error considerably, but still leave you with errors caused by the nonlinearity of the measurement process, temperature changes between the time of calibration and the actual measurement, etc.