As this sounds like a tutorial question and you are the student and this is an assignment... it is best you are guided over being given the answer...
- You have a date, great, turn it in to something useable with the Date() object.
- Your addition date, will this be in days or are you calculating time between two dates?
in response to question 2, if you are looking for time difference, then all you do is repeat the process like you did for the first date, subtract one from the other, then I suggest that you calculate in the "classical way" the amount of time that the difference is... as in years, months, days, hours, ..., ...
if Your response is adding days, then you would use the Date() Object methods to set the date by using the date today with the days ahead added to that value to then have the date() Object value pointer moved to that time, you then apply a date() method to obtain the desired data like years, months, hours, milliseconds and so on.
As for date formats, your date input should be controlled with the HTML5 form inputs that adds the date picker features needed. This date picker will put the date in to an ISO format which is YYYY-MM-DD format and if you set a date field, it expects the date to be in this format when you pass it the string.