I have recently inherited some property from my Mauritian mother, so I will do my best to explain the process.
If you wish to sell (without you ever owning it) your parents property, there is no need to acquire a Mauritian passport. Obviously if you do wish the property to be put in your name you will need one. I am selling 2 pieces of land and all I needed was a death cert, my British passport and 2 witnesses to certify I am the only child/beneficiary.
With regard to a Mauritian passport, you can apply through the Mauritius High Commission in London (takes approx 3 months) or directly in Mauritius (approx 7 days). There is however an age limitation (which I thought was 21) but at 25, I have managed to apply. A relative, in his 30s will have to apply directly with the government in person, in Mauritius.
Hope this helps!