Please try Media Go (preferences > output set to ASIO), dBpoweramp, and Exact Audio Copy then, and please tell us. They are all free.
I don't know. It is meant to work with windows devices, but I don't know enough to advise. Plus I have not tried the Mojo.
It might help you dicide if I post Mr Rob Watts explanation of the charging circuit here. This is a direct quotation,
"Just to clarify. Charging is automatic. If you are playing and charging at the same time, with a fully charged battery, the charger will supply enough current to balance the consumption used by Mojo, so no net current into the battery. If its fully charged and the unit is off, the charger will go off. The charger will re charge automatically when the battery voltage falls to 8.2v (off at 8.4v) so keeping the charger connected will ensure a full charge."
------
In other words as long as the battery is full it will not engage the charging curcuit. It the battery level drops a little it will charge for a while, when kept plugged in, on desktop.