You pay all costs and follow all normal timing rules for cards played from exile with Riku's triggered ability. For example, if the exiled card is a land card, you may play it only during your main phase while the stack is empty.

Modal spells printed prior to the Khans of Tarkir™ release didn't use bulleted lists for the modes; these cards have received errata in the Oracle card reference.

The X in Riku's ability is the number of times you chose a mode for the modal spell you cast, not the number of distinct modes you chose. For example, if you cast a modal spell that allows you to choose the same mode more than once and you choose the same mode three times, X is three and you may choose up to all modes of Riku's ability.

A spell is modal if it has two or more options in a bulleted list and instructions for a player to choose a number of those options, such as "Choose one" or "Choose one or more." Each of those options is a mode. Spells with spree are modal spells.

You can't choose the same mode of Riku's triggered ability more than once each time it triggers.