How can I strengthen my relationship with Allah and achieve khushūʿ (devotional humility) in acts of worship and lower my gaze, knowing that I have memorized the Qur'an and adhere to farāʾiḍ (obligatory acts) and nawāfil (supererogatory acts), but I do so without a heart, and I suffer from letting my gaze wander freely in a foreign environment?

You are on the right path as long as you maintain the obligatory prayers (Fara'id), the Sunnah prayers, and perform the night vigil (Qiyam al-Layl). The departure of khushu' (devotion/humility) may be due to certain sins, such as not lowering your gaze. If you do not repent and strive against yourself, you may lose your acts of worship. Strive to lower your gaze and remember your standing before Allah. Review the fatwas related to lowering the gaze and khushu'. Among the greatest aids to repentance is abandoning the place of sin. Emigrating from lands of فسق (immorality) and فجور (wickedness) may be a religious requirement and can help purify the heart.