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?