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What's the relationship between the DARPA phonetic alphabet transcription into an IPA transcriptions? Is it possible to map a transcription from one system directly into the other? Is it possible in one direction and not the other?
Is there software that does it in an automated way, so that I can map multiple words without having to do everything by hand?
Unfortunately, there is no "DARPA phonetic alphabet", at least not in widespread use. From the comments, you found the term here, and Microsoft's table seems to be giving examples of the ARPAbet, or ARPA phonetic alphabet (no D). I wonder if they care about errors in their documentation.
Wikipedia has a very nice table of ARPAbet and IPA correspondences. You want the two-letter codes; Microsoft is giving them in lowercase, separated by spaces. So a simple dictionary lookup can convert your text to IPA.
Translating in the other direction is usually possible, but not always: the IPA contains all sorts of symbols that the ARPAbet doesn't (since they don't occur in the specific dialect of English that the ARPAbet is designed to transcribe). But if you limit yourself to the subset of IPA that the ARPAbet can recognize, then another dictionary lookup is all you need.
EDIT: Looking at the examples in Microsoft's documentation, it seems like there's one other thing to keep track of: Microsoft's version of ARPAbet marks stress at the end of a syllable, while IPA marks it at the beginning. This complicates the process slightly, but only slightly, since the stress markings also divide the word cleanly into syllables. (By-book classic ARPAbet marks stress on the vowels, which means you have to divide up the syllables yourself.)
