RE: No kills?
If the targeted units are in a terrain such that they are concealed/ semi-concealed, then you will not 'see' any casualties. If the targeted unit is in clear terrain, then a number should briefly show over the targeted unit giving the number of casualties. Experience shows that this is typically a 0, 1, or 2, very rarely more (except, I hear in First World War).
So if your targeted unit is in a woods hex or building hex, for example, it may actually be taking losses, but you won't 'see' the losses. You do, however, ALWAYS see if a unit becomes "D" or "P" - - (do NOT ask me to explain the rationale! I'm just telling you how it is!)
If the target goes "D" or "P" then chances are you did cause a casualty.
Hope this helps!
PS let me or someone else know when you are ready for a PBEM game - - unfortunately, Tiller AI is notoriously inept!