Is it permissible to perform Hajj with money obtained by mortgaging gold, and is Zakat obligatory on mortgaged gold?

There is no objection to performing Hajj with borrowed money if there is sufficient gold or other assets to repay the debt in case of inability. Pledging is permissible by the Book, Sunnah, and scholarly consensus for securing a debt, and gold may be used as a pledge. If the pledged gold reaches the nisab (minimum threshold) and a year passes while it is in one's possession, zakat becomes obligatory on it because it is fully owned.