If you cast a spell for another cost "rather than pay its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If a spell has any mandatory additional costs, such as that of Stir Up Trouble, those must be paid for it.

If a spell has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

You must follow all normal timing rules when playing a land or casting a spell for cards exiled with Inside Information. For example, if an exiled card is a land card, you may play it only during your main phase while the stack is empty and only if you have an available land play remaining.