Just a few things I saw on your diagram that have been my mistakes in the past. Just an FYI not a bash
You screen should be powered from your computer. If it uses 12v dc than power it directly from the molex connector on the computer. THis will reduce the risk of line noise and help produce a better quality display. Your cars voltage is a little inconsistent and may cause poor quality video or even damage to your screen.
Make sure you have a large enough power supply for your carpc. Dont skimp on the PSU get a quality one right away, save some money buy spending some extra. Stay away from the M1ATX or M2ATX they dont have a very good life expectency and are not reliable. Get an opus and be happy.
As far as fuses go, depending on how much power you draw. Use this link to determine how much of a fuse you require.