Is it permissible for a niqabi to remove her niqab in a country where its inhabitants do not know her, in order to avoid people's astonishment or being called idols, or must she take pride in her religion and continue wearing it?

Covering the face and hands is a matter of scholarly disagreement, with the preponderant opinion being that it is obligatory to cover them. A Muslim woman should do so as an act of worship to Allah Almighty, not as a custom, and endure patiently, seeking His pleasure.