Did Iron Fist fight a dragon?

When Danny Rand was becoming the next Iron Fist, he defeated Shou-Lao by burning the dragon-shaped tattoo off his chest. After defeating Shou-Lao, Danny Rand plunged his hands into the brazier containing Shou-Lao’s immortal heart and it charged him with the power of the Iron Fist.

How did Iron Fist beat a dragon?

Shou-Lao (寿老) is the mythical dragon of K’un-Lun and the origin of the Iron Fist power. When Danny Rand defeated him by punching his molten heart, Shou-Lao made him the new Iron Fist.

Is there a connection between Iron Fist and Shang-Chi?

Their similarities would bring them together, as both Shang-Chi and Iron Fist are regularly featured in the anthology series The Deadly Hands of Kung Fu. When the two would eventually meet in Master of Kung Fu Annual #1, they established an immediate mutual respect for one another.