Is it permissible to go to the bathroom wearing a necklace that has the word "Allah" inscribed on it?

All Perfect Praie be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Anything that contains words pertaining to Allah, The Almighty, is desired to be left outside when going to the bathroom, or to be hidden for fear of losing it. And Allah Knows Best.

Is everyone obligated to follow the fatwas of his country, and if we adopt the fatwas of scholars of other countries, is it considered a sin?

All perfect praise be to Allah, The Lord of The Wolrds and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

It is permissible for the person who isn't specialized in Sharia sciences to apply the opinions of renowned scholars whom he trusts ,whether they be from his own country or not ,but if the scholars have different opnions regarding a certain issue/matter, then he must consult someone who is more knowledgeable than himself .It is preferable that you (the questioner) specify the case of your interest ,so that we could give you a more specific answer since some scholars deliver fatwas based on illogical/atypical opinions which should not be applied no matter what .And Allah The Exalted Knows Best.

What is the ruling on singing and listening to it while accompanied and unaccompanied by musical instruments?

Singing and listening to it unaccompanied by musical instruments is permissible as long as it isn`t practiced as a profession and is done by a man to other men, or a woman to other women with maintaining that no temptations are involved. The words of the song should be Islamic, and if temptation was likely to happen, then the singing becomes definitely forbidden. Temptation here means: whatever leads to committing a sin. In Islamic Sharia, singing accompanied by musical instruments such as the lute and the like is forbidden, and listening to it as well. The reason behind that is the fact that the musical instrument itself is forbidden. However, striking the tambourine and singing Islamic songs are permissible in weddings, circumcisions and the like.

Is Zakah(obligatory charity) due on rented property, and how is it calculated?

Zakah isn`t due on the rented property itself, but on the saved income from that property if it reached Nissab(minimum amount liable for Zakah), and a whole lunar year had lapsed over saving it.