Playing a card exiled with Colfenor's Plans follows all the normal rules for playing that card. You must pay its costs, and you must follow all timing restrictions, for example.

The turn you cast Colfenor's Plans, you have cast (at least) one spell that turn. After it enters and its last ability goes into effect, you can't cast any more spells that turn.

If an exiled card has morph, you may cast it face down.

If Colfenor's Plans leaves the battlefield, you can continue to look at cards exiled by it, but you can no longer play them.