How is Zakat calculated on money saved monthly to buy a house, and is Zakat obligatory on money lent to a struggling friend, the recovery of which is uncertain?

Your agreement with your friend to take a share of the profit in exchange for the loaned money is usury (riba), which is forbidden in Islamic law, because a loan should not bring benefit to the lender.

As for the zakat on your wealth: you must know the time when your wealth reached the nisab (the equivalent of 85 grams of gold or 595 grams of silver). If a full lunar year passes over it without it decreasing below the nisab, then zakat becomes obligatory on it. Money saved during the year is subject to zakat when a year has passed since you acquired it, or you can pay its zakat in advance along with your primary wealth.

As for the money you loaned to your friend: zakat is obligatory on it, but you are permitted to delay paying the zakat until you receive it, and then pay zakat for the past years.