Is Zakah due on the orphan`s money?

Yes, Zakah is due on the money of the orphan.

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.

What should a sick person, who is incapable of fasting, and who didn`t make up for missed fasting days, do?

One who has missed fasting days is obliged to make up for them, but if he/she wasn`t able to because of an incurable disease , or old age, then he/she has to pay a ransom which is feeding a needy person for each of the missed fasting days. And Allah Knows Best.

Is a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?

A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.