Does the Government of Mauritius pays for the fees for the Middlesex University in case the parent is retired ?

No, if someone chooses to go to Uni it is irrelevant if a parent is retired, fees need to be paid.

You used to be able to get grants but its very competitive now, grants are issued on parents household income and how well you are likely to do.

Answering your question directly, no this is not actually possible.

I don't think so. Unless it's University of Mauritius, social security can have a role.

If your friend has got 5 A at H.S.C then there is a great chance the government will be a sponsor.