How can one be certain that the Al-Raid Fund does not deal in usurious (riba-based) stocks, and is it sufficient to rely on the fatwa of Sheikhs Ibn Mani' and Al-Mutlaq that it is permissible, and on their supervision of it?

We have no knowledge of the true nature of the "Al-Ra'id Fund" to be able to rule on it. We have previously mentioned the permissibility guidelines in earlier fatwas. Those fatwas can be reviewed, and the fund managers can be asked to ascertain if it deals in interest-bearing stocks.