beammissile is a valid and working type. I presume it was going to be used for the Impossible Shot. It might be that it was buggy though.
I'm really not sure it does anything special at all. It animates like a missile, and I'm not sure it has the beam property of going through enemies to enable multiple hits.
beammissile seems to be different from beam insofar as it affects every square it passes through, like a beam, but stops when it hits an enemy or obstacle, like a missile. I used it for Degree in Dungeoneerings' teleport effect.
Not really. Description-wise it might be closer to being a beam, but if we are talking about system mechanics then it's definitely closer to a missile.