Is it permissible to receive a monthly financial allowance from the state, with the condition of repaying only half the amount after graduating, without any usurious interest?

If the loan is repaid without any increase, then there is no harm in taking it. The state is permitted to exempt the borrower from repaying all or part of the debt, as this is considered a donation. The fundamental principle of a loan is that it is initially a contract of donation. It is recommended for the lender to exempt a debtor who is in hardship. There is no harm in accepting a loan from a non-Islamic state, because accepting a gift or donation from a polytheist is permissible.