The cards are exiled face up. Casting the noncreature cards exiled this way follows the normal rules for casting those cards. You must follow all applicable timing rules. For example, if one of the exiled cards is a sorcery card, you can cast it only during your main phase while the stack is empty.

Any exiled cards you don't cast remain in exile.

If the card has {X} in its mana cost, you must choose 0 as the value for X when casting it.

You can't play any land cards exiled with Narset.

Because you're already casting the card using an alternative cost (by casting it without paying its mana cost), you can't pay any other alternative costs for the card, including casting it face down using the morph ability. You can pay additional costs, such as kicker costs. If the card has any mandatory additional costs, you must pay those.