I think that your conscious response to the news of this person's death was normal. Some sadness for someone you used to spend time with, but haven't seen for a while. Typically, the intensity of grief is related to how close, emotionally and "physically" you were to the deceased at the time of their death.
And yes, it seems likely that the dreams are related to this person's death. Subconsciously, you are aware of the deceased, and so they are with you again. The rest may be related to a heightened awareness of death, and mortality.
The dreams may be troubling, but they are only dreams. Ponder them as you choose, but don't worry about them, or your depth of grieving.