Statement (A):
Australia's renown for outdoor sports does not equate to a historical or cultural "proud legacy" in the same vein as yoga for India or martial arts for East Asia. Therefore, this statement is not technically considered part of a legacy.
Statement (B):
True. Yoga, originating in ancient India, is profoundly connected to Indian spiritual and physical disciplines. Despite its global recognition, it remains a proud cultural and spiritual legacy of India.
Statement (C):
False. Martial arts are primarily associated with East Asian nations like China, Japan, and Korea, not Germany. Germany lacks a historical reputation for developing or cultivating martial arts as a legacy.
Statement (D):
True. Gymnastics has historical origins in ancient civilizations, notably Greece and Rome, where physical training and bodily development were highly valued for military preparedness and cultural advancement.
Step 4: Final Answer
Consequently, only statements (B) and (D) are correct.