Does the time difference between Mexico City and Singapore change during the year?

No. The gap stays at 14h all year.

When is the best time to call Singapore from Mexico City?

There is no overlap between standard working days, so one side has to call early or late.

Mexico City is 14h behind Singapore. This gap is the same all year — neither city shifts its clocks relative to the other.

Mexico City

Mexico

--:--:--

Singapore

--:--:--

A 9-to-5 working day in Mexico City does not overlap one in Singapore at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Mexico City · Mexico	America/Mexico_City	UTC−6
Singapore · Singapore	Asia/Singapore	UTC+8

What is the time difference between Mexico City and Singapore?: Mexico City is 14h behind Singapore. This gap is the same all year — neither city shifts its clocks relative to the other.
Does the time difference between Mexico City and Singapore change during the year?: No. The gap stays at 14h all year.
When is the best time to call Singapore from Mexico City?: There is no overlap between standard working days, so one side has to call early or late.