[Clipper]

I believe you're right. It doesn't say to only go through the discards if you discarded a card, so you would go through them even if you lost nothing.

As for ignoring Time Warp, that's not errata as I see it. By saying to look for a card you can use and that it becomes yours, it means for you to look for a card you can have in use. You put the Item into play (not into your hand). You never have one-shot Items in use (despite the facts that you will eventually use them when you play them and that you can play them to the table before using them later). It's one of the subtleties of the wording that is a little confusing, but makes sense.

Note that you aren't looking for the first Item with a combat bonus either, you are just looking for the first Item that you can have in play that is not 'Usable Once Only'.