I see the internal battery runs at 3.7v, which is surprising when the MIFI accepts 5v USB for power. Is there a range that is supported (maybe 3.7v-5v)?
Well, USB is technically 5V ±0.25V, so 4.75V to 5.25V.
If you look inside the Mifi you will see the battery goes into a battery charging chip, so that handles all the voltage conversions.