Sorry for my late reply, because we make bma250 self-test in our lab.
From our test, bma250 x-axis value(Accl_x_pos_lsb: -45.3 Accl_x_neg_lsb:90.5), difference almost same with your test. We set range to 8g, so the result is(Accl_x_pos_lsb: -707mg, Accl_x_neg_lsb:1414mg), difference 2114mg >800mg(minimum difference).
For your new question, after product assemble, you could make self-test to verify if bma250 is ok. Reset sensor, then make offset compensation, avoid solder and assemble stress. For compensation, you could refer to BMA4xy-accelerometer-series-design-guide .
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