The voice only says "Hij" when you select the option to play the sentence slower.
The normal-speed version of this sentence is wrong, and needs to be re-recorded.
i think the audio says "Hij heeft de muis", not "een muis"!
Is muis used for the computer mouse as well?
Yes. Also "computermuis" if it isn't already obvious from context.
why heeft and not hebt
It's because hebben (to have) is irregular:
Ik heb, jij hebt, hij/zij heeft, wij (and all plurals): hebben.