I have three very different questions to ask:
No.1. How can I convince my mother to allow me to wear a Niqaab (I live in a non-Muslim country, and she's afraid for me, especially after the WTC).
No. 2. How do we invite people to Islam?
No. 3. How do we increase our Taqwa with Allah, both when we're praying and when we're not?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

1) With regard to covering a woman's face and hands, please refer to Fatwa 81554. Covering the whole body (except the two eyes) constitutes the preponderant opinion of the scholars.

Thereupon, you are not permitted to obey your mother concerning this issue. A person is not permitted to obey a servant if such an obedience constitutes a form of disobedience to Allah.

In other words, you can convince your mother, Allah willing, by reminding her of Allah's Commandment and the Prophet’s sayings in this concern. Also, you have to help her to learn that following Allah's Commandment is preferred to following a creature's order. In addition, you have to explain to your mother that the present events against Muslims do not entitle Muslims to commit what is forbidden, or to follow the rule of 'necessity makes permissible the prohibited things'.

However, if you believe that wearing the Niqab (face covering) may cause some unbearable harm to you, then you can follow the rule of 'Necessity renders what is forbidden lawful'.

Please, refer to Fataawa 81464 and 81642 about the rulings related to living in non-Muslim countries.

2) For your 2nd question, please refer to Fatwa 82520.

3) At-Taqwa (piety and righteousness) is the Divine percept to all people, in all places and at all times. Allah Says (what means): {And We have instructed those who were given the Scripture before you and yourselves to fear Allah.} [Quran 4:131]

At-Taqwa is the best provision to a human being on his way to the Hereafter. Allah Says (what means): {And take provisions, but indeed, the best provision is fear of Allah. And fear Me, O you of understanding.} [Quran 2:197]

At-Taqwa (to do what Allah orders and to avoid what Allah prohibits) can be increased through the following:

1 - To observe Allah's Commandments in private as well as in public.

2 - To preserve the prayer, whether the obligatory or optional one. The Prophet said that Allah Almighty has said: “My Slave does not get closer to Me with anything more beloved to Me than something that I have enjoined upon him, and My Slave keeps getting closer to Me by performing Nawaafil (supererogatory acts of worship) till I love him, and if I love him, I become his hearing with which he hears, and his seeing with which he sees, and his hand with which he strikes, and his leg with which he walks; and if he asks something of Me, I would surely give it to him, and if he seeks My Refuge (protection), I would surely protect him (i.e. give him My Refuge).” [Al-Bukhari]

3 - To keep company with the righteous people and to avoid the vicious ones.

4 - To seek refuge with Allah and to supplicate Him, since He does not disappoint anybody.

5 - To recite the Quran perpetually and to remember Him often.

As for al-Khushoo' (submissiveness and attentiveness in prayer), if one performs the prayer without al-Khushoo', then the prayer becomes just meaningless movements. We state that al-Khushoo' constitutes the spirit of the prayer. So, a Muslim has to do his best to perform the prayer with al- al-Khushoo'.

Al-Khushoo' can be gained through: Seeking Allah's help to gain al-Khushoo', supplicating Allah to grant a person this good quality, reciting more and more of the Quran, and doing one's best to comprehend the Quran and forms of Thikr (mention of Allah). Allah Almighty praises those who perform the prayer with al-Khushoo', as Allah Says (what means): {Certainly will the believers have succeeded. They who are during their prayer humbly submissive.} [Quran 23:1-2]

Also, one has to know that performing the prayer with al-Khushoo' helps one avoid misdeeds and abominable actions. One who loses al-Khushoo', finds no way to taste the sweetness of conversing with Allah while praying. It is a bad deed of a worshipper to think about worldly matters while he/she says in the prayer: “You alone we worship, and You alone we seek for help”.

Allah knows best.