As it always seems to in these threads, it depends on the type of vampire. In this case, it also depends on the type of screen.
If the screen works with a stylus, then even a dessicated-corpse sort of vampire should be able to use it. With a non-stylus-friendly screen, they’re probably out of luck, but other vamps might still be able to use the phone. Most of them look relatively human, which means they shouldn’t be all that dry under normal circumstances. Maybe they’d have trouble if they haven’t fed recently, and the tank was running low, but that generally seems to bring more serious problems than unresponsive touchscreens.
As for IR sensors, one fairly common trope is for vampires to be warm and/or flushed after feeding. Assuming the mirror business doesn’t interfere, a well-fed vamp should show up readily enough on passive infrared. Active infrared should generally spot them even if they’re at room temperature; it’s not looking for warm spots, it’s looking for changes in IR reflection patterns in the room–and no one has ever suggested that vampires themselves don’t reflect light, I don’t think.