Is this a shop where guests buy things?
No. Nothing is sold on the page and there is no store attached to it. It is a list you write, or one thing people can contribute to, alongside the collection options you set up yourself.
Can I ask for a cash gift toward a trip?
That is the most common use. Describe the thing you are saving for on the page, and contributions arrive recorded with the name of the person who sent them and whatever message they attached.
Do guests see what other people gave?
Guests see what you choose to show them: the list or the fund, and how to give. The record of who sent what, with their message, sits with you rather than on the invitation.
Can I add the gift section after invitations have gone out?
Yes. Edit the page, turn the section on and save. The link your guests already have shows the updated version, which is one of the few advantages of an invitation that lives at an address.
Does the gift section cost anything?
It is part of the birthday page rather than a separate product. What is included depends on the plan you are on, and the plans are laid out on the pricing page without any numbers quoted here.