What should a woman, who has given several births during different months of Ramadhaan, and didn`t make up for them in addition to forgetting the exact number of the days and years in which she had missed fasting, do ?

She should make up the days of Ramadhaan that she missed after estimating their number, and paying the ransom(in food) due on each day that she had delayed. She should also repay the ransom according to the number of years if she was able to fast before that time, but didn`t.

Should I pick up the newspapers thrown at the street because they definitely contain sacred names?

All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

The Messenger of Allah (PBUH) says: "Be mindful of Allah and He will protect you." Part of this is protecting whatever contains the name of Allah. Therefore, if you see a paper containing Allah's name thrown in the street, then you should grab it and similar papers, then burn them in a clean place. Doing so is permissible because Othman (May Allah be pleased with him) has burnt copies of the Quran which didn`t match the main Mus-haf. However, you aren`t required to collect every paper in the street. And Allah The Almighty Knows Best.

Is it incumbent on a wife whose husband hasn`t gone to bed with her(for sexual intercourse) for many years to observe `Iddah(waiting period) upon his death?

Upon the death of the husband, a wife is obliged to observe the `Iddah even if he hadn`t slept with her because she inherits him.

How should I be kind to my atheist father?

Allah, The Exalted, has decreed that we be kind to our parents, even if they are polytheists, by honoring and obeying them in all that isn`t sinful, so that they might love Islam and embrace it as a result.