Do the aforementioned circumstances—such as the inability to pursue studies, studies being the sole guarantee for the future, the lack of sufficient funds, the possibility of being forced to abandon acts of worship, and the inability to change abominable things—count as necessities that permit borrowing with usury?

The necessity that permits borrowing with usury is for the individual to reach a state where they face destruction, or are close to destruction, or endure an unbearable hardship. The excuses and justifications mentioned by the questioner are not considered necessity. However, if you are certain or highly assume that joining compulsory service will lead you to commit something forbidden, and you find no way to avert that except borrowing with usury, then there is no harm in that; due to the generality of Allah’s saying: "And He has already explained to you what He has forbidden to you, except for that to which you are compelled." The questioner should seek Allah’s help and try to find a good loan or convince his father to assist. As for benefiting from a usurious loan, if it is obtained, the prohibition pertains to the lender's liability, not to the loan itself. So, if the borrower uses it for a permissible purpose, then what he obtains is permissible. As for the forgiveness of the sin of borrowing, Allah knows best the sincerity of repentance, but the intention to repent does not initially permit committing the sin.