Did you check the day-month of your current birthday, or the day of the year? My birthday is April 8; that's the 98th day of the year (most years), which would be April 14 in the new calendar.
Starting the week on Monday seems more common than Sunday for most countries, I believe France does. And China and Japan name their days literally "Day 1" for Monday, ... "Day 6" for Saturday, and "Day Sun" for Sunday.
This is wrong. Saturday in Japanese is 土曜日, which is like "Earth day".
There's also "Sun day"(Sunday), "Moon day"(Monday), "Fire day"(Tuesday), "Water day"(Wednesday), "Tree day"(Thursday), "Gold day"(Friday), "Earth day"(Saturday). So your claim is wrong in Japanese for every day except Sunday.
If you see something written like 四日("4 day"), this refers to the day of the month not the day of the week(for Japanese).
Chinese uses the numbers for days of the week, so 星期一,星期二,星期三,星期四,星期五,星期六,星期日 for Monday to Sunday. They can use 周 or 礼拜 instead of 星期.
I remembered Japanese copied the Chinese at something there, but, whoops, it was the names of the planets that were copied. So the Chinese names of Mars(火星), Mercury(水星), Jupiter(木星), Venus(金星), and Saturn(土星) are copied onto the same days as planets that Romance languages name their days after.