How is Zakat calculated on wealth that has reached the nisab, given the existence of a long-term mortgage, income from colleague associations, and fluctuating annual profits? Is the value of the loan or its installments deducted? And how are amounts received shortly before the hawl (one year) dealt with?

The more cautious approach is to pay Zakat on all wealth that reaches the nisab, without deducting the value of installments.

The fatwa (religious ruling) states that debt prevents Zakat if there are no other assets (like real estate or a car you don't need) that can be used to cover the debt. There is no difference between immediate and deferred debt.

If you do not have other assets, you can deduct the installments from your wealth, and pay Zakat on the remainder if it does not fall below the nisab, while deducting genuine debt and not usurious interest if the loan was usurious.

Regarding money you receive just before the month of Zakat, if it is not profit generated from the Zakat-eligible wealth, you have the choice either to pay its Zakat along with the old wealth or to establish a separate hawl (Zakat year) for it.

However, if it is profit generated from the Zakat-eligible wealth, it is zakatable along with its principal.

In all cases, this new money is subject to Zakat, even if it does not reach the nisab on its own, because it reaches the nisab when combined with the original Zakat-eligible wealth.