Diamonds are the currency used in RoM's Item Shop, for most things. Normally, you would buy diamonds using our Recharge Diamonds link(s) on the main website page. They're bought using RL money, of course.
Others seem to have described the "gifting" system that is used between players to trade in-game gold for Item Shop things, or vice versa. Naturally, Frogster does not and cannot recommend using that system, since it can be dangerous to trade with people you don't know or are familiar with.
As for your other question above, there are items in-game known as "Daily Quest" items. You do not need to have taken a Daily Quest in order to find those items. You're welcome to keep or toss them, as you wish. You can use the Trashcan icon that's at the bottom of your Backpack (inventory)--open the Trashcan and right click on the items you wish to delete, then click on the Delete button, or you can drag them out of your inventory and drop them.
Most regular and Daily quest items are removed from your inventory when you turn in the quest. Some, unfortunately, are not, and have to be thrown away manually. And there are some quest items in the game which have an additional step in the deletion process. You'll probably run into a few of those. Fair warning, though: Most of the time, you can get away with abandoning a quest and picking it up again from the NPC where you got it in the first place. However, there are a few quests later in the game that can be permanently lost by abandoning the quest, or by deleting an associated quest item. This can ruin your character's progression through one or more chained quest lines. So, be careful.
Hope this helps.