There isn't any limit on the number of links you can include on a Bitly Page, but your account does have a monthly limit on the total number of links you can shorten. Any links you create specifically for your page count towards your monthly limit.
You can use any links you've already shortened on your page. Adding these to your page doesn't affect your general link limits, since you've already shortened the links.
Your monthly limits reset at the start of each month.