Answer to: How to repair itIf you don't have experience with mains electronics, I recommend just buying a new one.
Answer to: How to upgrade SD cardThe SD card, standing for Secure Digital, is a removable type of media. What you're talking about is the main memory storage built into the mainboard of the phone itself. To upgrade that, you need to replace the module that contains the memory chip (In most cases, that means the entire mainboard) with one that has a memory chip with a higher memory capacity. As the HTC one is a farily new phone and parts won't be common, the upgrade will be fairly expensive. I would recommend getting a USB On-The-Go adaptor which allows you to attach a USB drive for extra storage. I know it adds extra bulk but it's easier and cheaper
Answer to: Is my Digitizer or LCD screen broken?In this case the LCD is broken. The Digitizer is that part of the pannel that is sensitive to touch. The LCD actually shows the image. If there's something wrong with the image, it's the LCD. So to answer your question, the LCD is damaged