Non-Muslims choosing not to accept Islam

Q: Idol worshippers believe just as strong as a Muslim believes and also has prayers answered just as Muslims prayers get answered.

Hope you can help with this question as Allah can easily put and end to idol worship yet he keeps sending souls that get programmed into the faith they are born into and by clear observation the majority stay in that faith as they have strong reasons to do so. If a Hindu came to a Muslim and tells him to become Hindu and worship multiple Gods then the Muslim won't do that and vice versa. And just because the Quran says so is not good enough since anyone can put a book and say worship so and so but most will ignore that person and believe what they have been brought up with.

I'm sure you know what I'm saying and would be grateful if you can explain, but please don't explain with verses from the Quran, I want you to explain independently. 

Using any aayat of the Quraan as guidance when faced with difficulties

Q: Recently a sister mentioned that she has been practicing on a certain action which she heard from an Aalim. The practice is that whenever she faces any decision or difficulty then she opens the Quraan Shareef at random, and whichever aayah her eye falls on, she finds the translation and uses this as guidance. Is this permissible?

Distributing rent money among the heirs which include non-baaligh heirs

Q: Rent received from a house left in inheritance, the inheritors are:
wife
three baaligh sons and
one na-baaligh daughter
...all are living together presently sharing in the household items and meals together.

1. Can this rent money be used to buy all the groceries monthly? Can it be used to pay water and electricity bill?

2. When the sons marry and live on their own... and if the wife is left with one baaligh son and the na-baaligh daughter, how will the rent money be used correctly to fulfill the rights of all the heirs properly?

3. Sassa money, social grant from the government for two children, one is baaligh and one is not baaligh... It comes under the mothers responsibility for the children... Is it sinful for the mother to use some money from there for the household needs like food or house-hold cleaning items like washing powder or detergents?

4. Money kept in Al barakah bank for two children, one baaligh and one not baaligh... On a three month investment account which has profits every three month...the money is kept there for safe-keeping as the children are still minor to handle their own money in saving it... Is it OK if it's kept in the bank and the time it's needed and withdrawn then the profits on the original amount be given as charity... or is it better to just withdraw the money and close the bank account?