Islamic Practice

Is Salat al-Shukr (prayer of gratitude) or Sajda al-Shukr a valid Sunnah?

Sajda al-Shukr is definitively Sunnah — established by multiple authentic narrations. Salat al-Shukr (two rak'at) is at minimum permissible and not bid'ah, supported by hadith in Ibn Majah and the Prophet's practice at the conquest of Makkah. Salat al-Tawba is definitively Sunnah with a clear authentic hadith.

What happens if you make an oath in Allah's name and cannot fulfill it? What is the kaffarah?

If you make a sincere oath by Allah and cannot fulfill it, you must pay kaffarah: feed 10 poor people, clothe 10 poor people, or fast 3 days. If you see a better alternative, pursue it and still pay kaffarah. Intentional lying while swearing by Allah is a major sin requiring only sincere tawba.