different result for yyyy-mm-dd and yyyy/mm/dd in javascript when passed to "new Date"

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Answer 1

It boils down to how Date.parse() handles the ISO-8601 date format.

The date time string may be in ISO 8601 format. For example, "2011-10-10" (just date) or "2011-10-10T14:48:00" (date and time) can be passed and parsed. The UTC time zone is used to interpret arguments in ISO 8601 format that do not contain time zone information (note that ECMAScript ed 6 draft specifies that date time strings without a time zone are to be treated as local, not UTC)

Your first date format 2015/03/31 is assumed to be March 31st, 2015 at 12am in your current time zone.
Your second date format 2015-03-31 is seen as ISO-8601 and is assumed to be March 31st, 2015 at 12am UTC time zone.

The "Differences in assumed time zone" heading from the linked documentation goes into a bit more detail:

Given a date string of "March 7, 2014", parse() assumes a local time zone, but given an ISO format such as "2014-03-07" it will assume a time zone of UTC. Therefore Date objects produced using those strings will represent different moments in time unless the system is set with a local time zone of UTC. This means that two date strings that appear equivalent may result in two different values depending on the format of the string that is being converted (this behavior is changed in ECMAScript ed 6 so that both will be treated as local).