Is it permissible to perform Umrah before fully paying off a car loan, and will a person be detained in the fire of Hell if they die while owing an unpaid debt?

There is no harm in performing 'Umrah (definition) for a debtor if he is confident he can pay off his installments. A debtor is not withheld in Hellfire, but rather from entering Paradise until his debt is paid off; due to the saying of the Prophet, peace be upon him: "The soul of a believer is tied to his debt until it is paid off." Al-Qari mentioned that the meaning is that he will not attain his goal of entering Paradise or a high rank, or his soul will not find pleasure as long as he is in debt. Then it was said: The debtor who is withheld is one who borrowed due to foolishness or extravagance. As for one who borrowed for a rightful obligation and did not leave behind enough to repay, then Allah will not withhold him from Paradise, Allah willing.