Is Zakat obligatory on money invested in purchasing lands for construction and sale, given the existence of accumulated debts, and how is Zakat calculated on the remaining lands, and is it permissible to count a debt owed by an insolvent person as Zakat?

The house you lived in is not subject to Zakat. Zakat is due on the remaining amount of its sale price, after debt repayment, if it reaches the nisab and a hawl (one lunar year) passes.

The lands you purchased with the intention of building on them and renting them out are not subject to Zakat, even if you change your intention and sell them. Zakat becomes due on their price if a hawl passes while it is at the nisab.

However, if you intended to build on them and sell them from the outset, they are considered trade goods, and Zakat becomes due on them if your share reaches the nisab and a hawl passes on the original capital. They should be valued at their market price when the hawl passes, and one-quarter of a tenth (2.5%) should be given.

The debt owed to you by your insolvent neighbor does not waive its Zakat obligation. Zakat becomes due on it when you receive it. You should then pay one-quarter of a tenth for each year, or for a single year, according to a difference of opinion.

It is not permissible to count the debt owed to you by an insolvent person as Zakat and forgive it in exchange for your Zakat obligation, according to the more sound of the two scholarly opinions, though some scholars permit it.