Taking just the 20th and 21st centuries, the following years have the same day/date combination as 1999:
1909, 1915, 1926, 1937, 1943, 1954, 1965, 1971, 1982, 1993, 1999, 2010, 2021, 2027, 2038, 2049, 2055, 2066, 2077, 2083, 2094 and 2100
The next year that has the same day-date combination as 2011 is 2022.
Yes, the year 2094 will have the same day-date selection as 2010.
A coincidence
The most recent year with the same day-date correlation as 1980 was 2008. The next year with the same day-date correlation as 1980 will be 2036.
Prior to 2011, the last year with the same day-date arrangement was 2005. After 2011, the next one will be in 2022.
Since 1965, the years with the exact same day and date combinations were: 1971 1982 1993 1999 2010 The next one will be 2021.
2036
1981
No
The most recent year was 2002. Coincidentally, Easter falls on the same date in 2002 and 2013.
September and December of the same year have the same calendar except that September has 30 days and December has 31. The last 31-day month before December of a regular year that has the same date to weekday relationships is July of the previous year. The last 31-day month before December of a leap year that has the same date to weekday relationships is October of the previous year. The first 31-day month after December of the year before a leap year with the same date to weekday relationships is the following March. The first 31-day month after December of the second year before a leap year with the same date to weekday relationships is August of the leap year. The first 31-day month after December of a leap year or the year after a leap year with the same date to weekday relationships is March of the second year after.
It was 15th August 2000. Same day as Indian Independence day.