How are gaps filled during congregational prayer?

A praying person is allowed to take two steps in order to fill the gap in the row ahead. If the distance was long and requires much movement, then it is impermissible for one to move to fill it because much consecutive movement (three movements) during prayer invalidates it.

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.

Is it permissible to thin the eyebrows or remove them and draw in their place?

Thinning the eyebrows, removing them, and drawing in their place—known as Namas—is prohibited. The Prophet (peace be upon him) cursed those who do it. And Allah Knows Best.

Is it permissible for a Muslim woman to leave her house adorned and without wearing her proper Islamic attire?

A Muslim woman isn't permitted to leave her house adorned and without wearing proper Islamic attire. And Allah Knows Best.