What is Master Yi's most reliable build when he mainly has to reach the first reset without being cut off?

The most reliable build on Master Yi is the one that preserves the first spike while still keeping an escape valve. If your item order prevents you from playing the champion's first real window, the build may look strong on paper but it is not reliable.

When should you truly adapt Master Yi's build instead of simply pushing the standard carry version?

You should adapt as soon as the enemy draft stops you from playing the timing the build was meant to serve. If you need to survive longer, absorb more poke, or answer a specific engage pattern, the purchase order must move before you even think about the final six-slot build.

Which enchant should Master Yi choose when the real issue is mainly preserving chase rights after entry?

quicksilver is often the most stable choice because it directly supports this game plan: reach critical dps threshold to snowball fights through resets.