The playlist will take up memory if it is syncing any songs you own locally on your computer. It will take up as much space as the normal song(s) would if you were to sync them some other way (like through iTunes). However, playlists that only contain songs that you DO NOT have locally (one that only stream from Spotify) do not take up any space to my knowledge.
The advantage of having Spotify (especially on devices such as iPad) really comes with a premium account. You can stream music you don't own first of all. You can stream the music free (with ads) with a free Spotify account ONLY on your computer. If you want to stream any playlists on your phone of music you don't own, you have to have a premium account.
I think the above answers all your questions. Ask if anything is unclear or if you have more questions 🙂