What is my duty towards my family and parents, especially given the difference in our creedal approach and their threat to cut off financial support, and how can I rid myself of lying, which has become a habit, and what is the way to restore self-confidence and focus in studies and worship?

You must combine honoring your parents with advising them. Filial piety is obligatory, even if they command shirk (definition), but it is not permissible to obey them in that.

You must stop lying and adorn yourself with truthfulness, for lying leads to immorality and Hellfire, while truthfulness leads to righteousness and Paradise. Seek Allah’s help, and remember that Allah hears, sees, and records every word and deed. Always strive for truthfulness and avoid lying, for it incurs Allah's wrath.

Your diligence in memorizing the Quran and studying religious knowledge is an incentive to adorn yourself with the manners of the people of the Quran, such as tranquility and dignity. Permissible joking is that which is not excessive and does not lead to harm or loss of respect.

We advise you to combine studying medicine with Islamic sciences, for medicine is a communal obligation (fard kifayah), and your being a doctor increases the credibility of your da'wah (call to Islam). Beware of abandoning your current studies for a fleeting idea, as many have regretted doing so.