The day, month, and year functions each return a number (not a formatted string) so using them won’t give you leading zeros for single-digit days or months. It could be done by setting the numberFormat, but for what you want there’s an easier way, using the formattedTime() function. This should do what you want:
TypeText formattedTime("%d%m%Y", TheDate)
The formatting codes that you can use with this function are described in the documentation for the timeFormat global property.
Regarding your other question (adding a year to a date), SenseTalk’s predefined time interval values only go up through weeks, and don’t currently include months and years since they aren’t a consistent number of seconds long. To get a date that’s a year in the future, you can add 365 days, except of course that won’t be correct for leap years.
So to correctly add a calendar year, the best approach is probably to convert to the dateItems format, which separates the date into separate values for year, month, day, and so forth. In this format you can add or subtract any number of years, months, days, etc. by dealing with the appropriate item. Then convert back to the final format that you want, like this:
set myDate to today
convert myDate to dateItems
add 1 to item 1 of myDate -- item 1 is the year
convert myDate to short date -- or whatever format you want
The dateItems formats are often overlooked, but can be quite useful for doing this sort of calculation.