Calendar and Javascript

Have already a calendar on my web-site but want to do some more things with Javascript. You can find the calendar on the top-left corner at [login to view URL] . Below are the things needed: 1) When CheckIn date is entered through Calendar or drop-down menu then CheckOut date should go one day later (in case it is empty or selected at a previous date). Now it stays the same both at Calendar and drop-down menu. At this point someone should be careful for the last-days-of-month-changes and last-day-of-the-year changes. 2) When the calendar is first opened and "next month" is clicked on the arrow at top right then 1 click is "lost". So someone has to click twice in order to go to December. Then every click moves you to the next month. So 1 click is lost in the beginning of the process. 3) Please open the calendar and move to a next month but do not pickup a date. Then close the calendar. Then re-open this. It opens to the month that you left it before closing it BUT if you click to the next month it begins again since November. WHY??? 4) Only in Mozilla when someone puts a name in the field on top left corner and press Enter then the calendar opens(instead of the form to be submitted). Can it be corrected? Thank you for your help.