What should one who made an intention, at night, to make up for a missed fasting day, but broke his fast on the next day?

One who started making up a missed fasting day, then broke his/her fast without a legitimate reason is considered sinful, and is only obliged to make up for the missed fasting days. And Allah Knows Best.

My Husband Works as a Diver and most of His Client are non-Muslims. Is his work permissible or not?

There is no harm on his job. 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 swearing a false oath by the Holy Quran?

Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.