Hello ! Thanks for playing my game !
I get that asked a lot, that means it's not clear enough in the game ^^
In the next update I'll fix items clarity.
For Gifts and Love Letters they are to be used in the girls route. For example on Tanuki's route at step 10 you must pay a Love Letter to progress and unlock a new card.
As for the succubus ticket, you can use them in the battle shop, a special room you can encounter during battle. You don't need to have them in your inventory, as long it's in your stash it's good.
Thanks again !