How is the Zakat calculated on the following:Cash in banks,house for personal use, house for rent, house can be rented or for personal use, land bought for building another house, land bought for summer holiday, land for trade, personal belongings, shares investments.Can I consider the monthly payment for my brothers' family/children as partial payment of the future due zakat?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

1- Belongings that are for personal usage such as a house to live and a land for building a house (even another house) or to use it as a summer residence are not subject to Zakah.
A land bought for trade and all cash are subject to Zakah as long a their value reaches a Nisaab (the price of 85 grams of gold) and they have been possessed for one lunar year (Hawl). By the way, it is Haram to deposit money in usury-taking-banks.
As for Zakah on shares invested in some business, check our Fatawa: 84386 and 85138.
As for a house prepared for rent, its revenue is subject to Zakah as stated within the two conditions of Nisaab and Hawl, whether you add them or not to other property.
2- It is permitted to give Zakah in advance if there is need as you stated in your question. But, we draw your attention that Zakah becomes null if you give it to those persons whom you are to maintain, such as wife, children…; otherwise, it is sufficient. Then, if you give Zakah to those whom you are to maintain, this makes you benefits from it and this is against the goal of Zakah, helping the needy.
If you give Zakah to your relatives, this will be a charity and a good deed to your relatives.
More details see Fatwa 82489.                                         Allah knows best.