Is zakat obligatory on a house purchased with the intention of preserving wealth and securing livelihood from its annual rent of 7,0 riyals, while there is still an unpaid debt?

If the house is for personal use and not for trade, there is no Zakat on it. Zakat is only due on its rent if a year passes while it is in your possession and it reaches the threshold (nisab). However, as long as there are debts you cannot pay, there is no Zakat on the rent until after these debts are settled and a nisab remains upon which a year has passed. The majority of scholars hold that debt negates the obligation of Zakat on inner wealth (gold, silver, money, and trade goods).