You need one affiliate ID for each website (not each page). As long as the referral is made on the same domain, your affiliate link will be valid.
However, even may it be on the same domain, if the referral appears from an entirely different website or pages which do not share common objects/contents with the home page at all, it may lead to a refusal of payment or suspension of your affiliate ID. In such a case, you will need to apply for another ID.
Affiliate links are valid for 30 days from when the affiliate link was clicked. However, as click information is cleared once a purchase is made it will not necessarily cover all purchases made by the clicker within one week from the click.