HMM's - Possibility?
HMM are useful for sequence modeling and classification - problems for which your observations unfold on a 1-D axis in time or space. Hence their usefulness for speech recognition, because a word is a sequence of heterogeneous states corresponding to its various phones. But the problem of recognizing whether a speaker is male or female doesn't really have this sequential aspect, so HMM would be indeed an odd approach for it. One good way of finding out whether HMM are a good fit for a problem is the following: would you still be able to perform the classification if the data is shuffled? If you take a speech recording, break it into segments and shuffle them, you won't be able to recognize the words spoken, but you will still be able to recognize whether the speaker is male or female, and indeed identify this speaker.

I am not sure about the bat question - are you talking about recognizing animals from the sound they emit? Or else, from what kind of data? Does this data have a sequential structure?

It seems to me that what you want to do is, from a broad point of view, machine learning or pattern classification. HMM is a very specific solution to machine learning problems (those related to classifying processes unfolding along a 1-D axis), but this is by far not the only tool! Maybe you should learn more about the other approaches (bayesian methods, support vector machines, neural networks, decision trees...), and the specifics of each data types (features for image, audio, text...).