Is what I am doing correct, after wearing the niqab despite my parents' rejection? And am I sinful if I disobey their command not to go out [wearing it]? And did I make a mistake when I wore the niqab without informing them?

Covering a woman's face is obligatory. If a woman commits to wearing the niqab, she is not considered disobedient for contradicting her mother in this matter, because there is no obedience to a creature in disobedience to the Creator. In this case, it is better to stay at home and not go out except out of necessity, based on the Almighty's saying: "And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger. Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [complete] purification." This is safer and more protective for her from temptations, and it avoids conflict with parents, while also recommending kindness and beneficence towards them to win their affection.