Why should a prayer be done for expressing gratitude?

Prayer is actually a synonym for surrender. This act of surrender is completed only after the expression of gratitude. Gratitude is a means of offering the doership of an act to God / the Guru; hence it helps in reducing the ego.

Diwali (Deepavali)

The word Diwali has originated from Deepavali, which in turn is formed as deep (lamp) + avali (row). Deepavali is thus a row of lamps. During Diwali, lamps are lit everywhere.

Vijayadashami: The triumph of righteousness

Vijayadashami is also known as Dashhara, Dussehra, Dassera, Dashera, etc. On this day, that is the tenth day of Navratri, Deity Shriram won victory over Ravana by killing him. It is one amongst the three and a half auspicious periods.