Is the amount received from a university grant, without it being claimed, considered a discharge of one's obligation towards Allah and fulfillment of the commitment to the Ministry? And is Zakat due on it, or should one await the state's claim for it? And is it permissible to use it in a project that involves an interest-based loan?

If the ministry agrees to terminate the contract and waive the amount it received, then it must be ensured that it will not claim it in the future before disposing of it. The zakat for this amount is obligatory if it reaches the nisab and a full year has passed over it, even if you intend to return it.

It is permissible to partner with a usurer or someone whose capital originates from an interest-based loan, because he owns what he borrowed, despite his sin. However, it is more preferable to partner with a righteous Muslim.