How to write codes so that the days do not exceed 28/29/30/31 days per month? and also leap year??

You don't. It's already been done. I use DateTime. Date::Calc is mentioned frequently.

The program should accept [...] the day of the week for January 1 of that particular year

That's not necessary since you have ->dow().

sorry i dunno the html formatting

On this site, <p> at the start of paragraphs, and <c>..</c> around computer text (code, data, output, etc).