Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
What is the ruling on a Muslim who slaughters an animal while being in a state of Janabah(ritual impurity)?
Slaughtering is permissible for the ritually impure man and the menstruating woman because ritual purity isn`t a condition for the validity of the slaughtering. Moreover, it is permissible for the uncircumcised person to do the slaughtering as well.
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 to fish on Saturday?
It is permissible for Muslims to fish on any day, but the sons of Israel are the ones forbidden to fish on Saturday. Moreover, there is no evidence in Islamic Sharia prohibiting Muslims from fishing on that day.