Neither seems ungrammatical to me, though I would vastly favor the first sentence over the second. The phrase all the time makes this a little bit harder, as it has a literal interpretation (at all possible times) and a colloquial interpretation (very often).
The first sentence, with has been crying all the time, suggests that the baby was crying in the (recent, from context) past and is still doing so in the present. The context of the sentence suggests to me that the crying is not the typical state for the baby, and that there is a presumption that the listener/reader will do something to address the crying.
The second sentence gives the impression that crying all the time is a typical behavior for this particular baby. Is crying indicates crying at the present moment, and including all the time in the same sentence suggests that the baby is always crying at the present moment. Which is to say, the baby is always crying. In this case, the Where are you? question seems less meaningful to me. If the baby constantly cries, what good would my presence be? Would it really be so surprising that I would be anywhere other than where the crying baby is? This sentence suggests to me that there is information I'm not getting from the text as written, in which case the sentence itself could probably be changed and improved.
Your final sentence is correct in that it can be parsed appropriately, but whether or not it is better than another depends on what you'd like to express. Babies are crying all the time would mean that some group of babies (possibly all babies anywhere, ever) are crying constantly (or frequently, as with the colloquial interpretation of all the time). Babies cry all the time would be understood as "frequent crying is a typical behavior of babies", and carries no suggestion that babies are in the middle of crying at all possible moments.