وعليكم السلام ورحمة الله وبركاته
1) Imaan is belief in Allaah Ta`aalaa, all of the revealed Kutub, the Malaa'ikah, Jannah and Jahannam, all of the Rusul (Messengers), in the Day of Qiyaamah, in the resurrection, etc.
2) Taqwa is fear of Allaah Ta`aalaa. Fear which causes you to abstain from what is Haraam and to do what you have been commanded to do.
3) Imaan can exist without Taqwaa, but Taqwaa can never exist without Imaan.
4) The likes of me, an evil person, have no right to speak on Taqwaa. However, I can tell you what Allaah Ta`aalaa says in the Qur'aan:
والذين اهتدوا زادهم هدى وآتاهم تقواهم
"And those who are guided (i.e. those who accept and follow the guidance of Islaam), He (Allaah) will increase them in guidance, and He will grant them their Taqwaa." [Soorah Muhammad, 47:17]
Abstaining from sin and doing good deeds, along with Du`aa to Allaah Ta`aalaa to increase your Imaan, will result in your Imaan being increased. The same goes for Taqwaa. Taqwaa is to fulfill all obligatory duties and to abstain from sin. The more you do this, the more Taqwaa you have.
والله تعالى أعلم