Is it permissible to give out a portion of the money deposited in the bank with interest, after furnishing the apartment and getting married? And is what the brother did, by taking a portion of the amount on the pretext of usury, correct?

The father has not wronged his elder son by specifically allocating money to his younger son for a necessary reason, and not merely out of favoritism. If the elder brother is content with this, then there is no harm.

Usurious gains are forbidden (haram), and it is not permissible to deposit money in usurious banks. The decrease in the value of money does not justify owning usurious gains. The brother's action of getting rid of usurious gains is correct, and it is possible to ascertain their amount.