Fascinating thread.
Ming ships were far in advance of western ships of the time. While the size of Zheng He's treasure ships is probably exaggerated, they were still much larger than anything seen in Europe since the Romans.
- They could sail into the wind
- The battened sails were resistant to major tearing
- The nature of the sail plan took advantage of aerodynamics to create "slots", which increase sail power and efficiency
- They had flood resistant transverse bulkheads, possible watertight.
- Fore and aft compartments may have been free flooding which could aid in stability, reducing pounding and pitching
- While having very high freeboard, they also had shorter masts. This could have lowered the center of effort and reduced the effect of heeling.
- The use of leeboards added to directional stability and mitigated the effect of crosswinds due to the high freeboard.
- The fenestrated rudder reduced the effort required in steering.
There are more areas where the Chinese were way ahead of the Europeans in marine technology. They had been navigating the Indian Ocean for centuries and were accomplished mariners.
Regarding the condition of the crew upon arrival in the west, I think that they might have been in quite good shape, considering that it was not uncommon to grow produce onboard during long voyages. In any case, the Europeans were familiar with the effect of a long sea voyage on crews health and moral, so I don't think they would have been too surprised by a tired crew. Since the fleet contained water ships and supply ships, it is more likely that the fleet would arrive in fairly fresh condition.
The Chinese also brought equine carriers and had their own horses. They had long exposure to Arabia and India and were probably familiar with their very fine breeds, so perhaps the only horses they might be interested in were European draft animals (I don't know if the Chinese had any equivalent).
The wealth and power of Zheng He's fleet would have had a massive effect on Europe I expect. I believe that it might have even spurred exploration westward as nations, now more certain of the wealth of the east tried to find a way to get there. The Portuguese, who were already wandering down the west coast of Africa, would continue in that direction because they would know it could be done. Perhaps the English or French, wanting a piece of the pie wpiould have followed their fishermen, already on the Grand Banks, west and discovered the New World earlier.
I think the effect on China would have been more restrained, but the Ming's might not have been able to ignore these barbarians for long.
This is a great WI.