1) Your question is related to whether it is permissible to lease your property to a bank company.
Mufti Rasheed Ahmad Ludhyanwi writes: “To lease a property to a bank is Makrooh Tahreemi, however, to give it to a Non-Muslim is Makrooh Tanzeehi.
If he makes the condition that the rent will be paid through Halaal funds then still the leasing will be Makrooh, however, he would be saving himself from Haraam funds, he will only be sinful for the leasing transaction”. (Ahsan al-Fataawa, p. 305, v. 7)
It is advisable for him to sell it to avoid a Makrooh transaction, as a Makrooh that is persistently practised becomes Haraam.
2) a) Zaid can still be considered a Faqeer, eligible for Zakaah funds, even if he lives with his parents, providing he meets the definition. He does not possess wealth of any kind that maybe equivalent to that of the Nisaab rate.
b) It is Makrooh to give Zaid an amount so high as Zakaah that would make him a possessor of Nisaab. (Ahsan al-Fataawa, p. 304, v. 4) In your question you mentioned Salim giving Zaid enough money for him to buy a home as Zakaah, this would be Makrooh, as obviously this amount would exceed the Nisaab amount.
c) If Salim gave an amount as such, it would be Makrooh, however, his Zakaat has been fulfilled.
And Allah knows best.
Mufti Yaseen Shaikh