The original Eddie was just this theatrical mask. You can kind of see it in the band photos on the first album and also on the "Running Free" single picture sleeve. It's a face right next to the band logo. It was connected to a pump that would spurt out various kinds of liquids and it would drool all over Doug Sampson or Clive Burr or whoever was at the drums that time. People would also try to sling stuff into it. Its full name was "Eddie The Head" (Edward T.H. on the "Live After Death" cover) and it comes from the following old joke :
Eddie was born with no body and no arms and no legs. Just a head. But despite this slight birth defect his parents loved him very much cared for him and were always giving him all these presents like hats and blow things at parties and other cool stuff. So on his sixteenth birthday they run into a doctor that says "Hey, I can give Eddie a body" so the parents are going totally nuts because finally their kid can have a body and be like other normal people. They go home and are really excited and say "We have got a surprise for you. It's the best present ever !" and Eddie says "Oh, no, not another fucking hat !"
They gave the name "Eddie" to that mask. By the time of them being signed to EMI Records, they got Derek Riggs to do cover artwork. The first was the cover to the "Running Free" single, and you see that zombie in the back missing an arm (which somehow is in front of a guy who looks a lot like Bruce Dickinson running away from that zombie). The band liked the zombie guy so much that the name Eddie was transferred over to the zombie when they lost that mask with the pump.
Derek Riggs trademark symbol is something like the following. It seems to be his initials...a (mirrored) D, and the R on the right-hand side. Or something like that !
/--|--\ / | \ \ | / \--|--/ \ | \ .--, | \--, |__| | |__| \./
The Fear Of The Dark illustration was not done by Derek Riggs. According to page 15 of the CD booklet: "Illustration : Melvyn Grant". I don't know if Melvyn Grant is a total unknown, or if he has done other work or not...
You can find the letters "MEL" printed a bit to the right of where Eddies foot should be. I suppose that is the way he use when signing his artworks... According to an interview with Bruce Dickinson on MTV shortly after FEAR OF THE DARK was released, they picked three different artists to do a cover for the album, and they would pick the best one out of the three submitted. He went on to state that Derek would still be involved with future artwork and that he wasn't fired or anything).