Are minors (persons under the age of puberty) obliged to fast?

A male under the age of puberty isn`t required to fast, but his guardian should order him to fast if he was able to endure the hardship until he gets used to it. And Allah Knows Best.

What is the ruling on a vowed animal sacrifice?

A vowed animal sacrifice is to be distributed amongst the poor and needy, and neither the vow-maker, nor those supported by him are to eat from it.

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 permissible for a person who has to make up for missed fasts to fast six days of Shawal (the month directly after Ramadan) before making up for the missed fasts ?

Yes, it is permissible for him/her to do so, but it is better that they make up for missed fasts first. And Allah Knows Best.