I noticed that many "month calendars/date pickers" start with Sunday and end with Saturday in the header - Is this a standard in the western world or is it a convention or is there any reason behind this?
According to the International Organization for Standardization, Monday is considered the first day of the week.
The ISO week-numbering year starts at the first day (Monday) of week 01 and ends at the Sunday before the new ISO year (hence without overlap or gap). It consists of 52 or 53 full weeks.
That being said, I do not have an answer as to why so many datepickers have a Sunday default week start.
In the US, the standard week is considered to start on Sunday. So calendar pickers created using the US standard will follow the same convention. I believe many pickers can be changed so the week starts on Monday, but if the web designer is also from the US, I wouldn't expect them to add that option.
Although ISO define Monday as the first day of the week, there are cultural differences. According to First Day of the Week in Different Countries at ChartsBin.com – which shows a nice map of the world as well as listing the first day of the week for 108 countries – the world divides into three categories:
Monday: 61 countries, predominately Europe, Russia, India, S.E. Asia and Australia.
Sunday: 32 countries, predominately USA, Canada, most of South America, China and Japan.
Saturday: 15 countries, predominately North Africa and the Middle East.
Note: The chart does not show any preference for most of the countries in Africa.
Although as pboss3010 says in their answer, if most date-pickers start with Sunday, it was probably because the first data-pickers were written by, or for, the US market (and/or before internationalisation was "a thing").