No, Wishpicks doesn't ship gifts and never handles payment. The gifter buys the item at the store, pays for it and any shipping there, then arranges delivery directly with you.
Wishpicks helps people choose the right gift. It isn't a shop, so there's no cart or checkout for gifts on Wishpicks itself.
How a gift gets to you
A gifter opens your shared wishlist and picks an item to Reserve. Reserving just marks that they plan to get it.
They click through to the store and buy it there. Whatever that store charges for the item and shipping, the gifter pays at the store's checkout.
They arrange delivery with you. They can ship it, bring it in person, or ask where to send it.
What to expect
Reserving doesn't fulfill the wish, and it isn't a purchase — Wishpicks never confirms a real purchase at the store. A Reserve badge means "someone plans to get this," not "this has been bought." You'll mark an item as received yourself once it actually arrives.
Shipping cost, speed, and where it ships from all come from the store the gifter buys from, not from Wishpicks.
Wishpicks has no delivery-address field, so share where to send a gift privately. See How will someone know where to send my gift?.
What about Wishpicks Plus?
Wishpicks Plus is the one paid thing on Wishpicks, and it's only about price tracking. It doesn't buy, ship, or deliver gifts, and it has nothing to do with shipping costs.