Is it permissible to take a loan from the American government to study computer science, knowing that the installments are convenient and extend up to fifteen years, and am I obligated to repay these exorbitant amounts after completing my studies?

If the loan is qard hasan (definition) (interest-free), then there is no objection to it, and the remainder must be repaid in a single payment or in installments from your country. However, if it is interest-bearing, then it is riba (usury) and prohibited. It must be repaid, but without paying the usurious interest, unless you fear punishment. It is not permissible to take money and then not repay it upon leaving the country, because a Muslim is obligated to fulfill the covenants and contracts they have entered into, as Allah Almighty says: "O you who have believed, fulfill [your] contracts."