I believe in my entire life I've encountered exactly one situation in which the day that is defined as the first day of the week actually made a difference to anything: my kids' swim school schedule, where Week N of the term runs from Sunday through to the following Saturday inclusive.
Since the working week (and the school week) here starts on Monday regardless of whether Sunday or Monday is regarded as the first day of the week, it seems to have always been a distinction without a difference to me.
Yes. Putting the year first and with 4 digits is the only safe way because, afaik, nobody anywhere uses yyyy/dd/mm. It's nice that it's also in order of significance but the main advantage is unambiguousness.
You'd think people would have learnt from Y2K but somehow we still see 2-digit years which make dates like 03/04/05 impossible to even guess at. It's slightly better since 2012 where a 2-digit year can't also be a month, but we'll have to wait till 2032 for 2-digit years to unambiguously mean year.
This is an area where I believe localization makes things worse, not better. If every website showed dates with the year first, people would easily understand, regardless of whatever silly local convention they have. As it is, whenever I see a ##/##/## date, I have to think about what the website might be trying to do (do they know what country I'm from? What country I'm in now? Are they using their own local convention?) and what possible dates it might mean. "I think that happened around August, so 08/10/14 is probably not the 8th of October." Localized dates just make no sense at all on the internet.