How can I specify the format of AVAudioEngine Mic-Input?

You cannot change audio format directly on input nor output nodes. In the case of the microphone, the format will always be 44KHz, 1 channel, 32bits. To do so, you need to insert a mixer in between. Then when you connect inputNode > changeformatMixer > mainEngineMixer, you can specify the details of the format you want.

Something like:

var inputNode = audioEngine.inputNode
var downMixer = AVAudioMixerNode()

//I think you the engine's I/O nodes are already attached to itself by default, so we attach only the downMixer here:
audioEngine.attachNode(downMixer)

//You can tap the downMixer to intercept the audio and do something with it:
downMixer.installTapOnBus(0, bufferSize: 2048, format: downMixer.outputFormatForBus(0), block:  //originally 1024
            { (buffer: AVAudioPCMBuffer!, time: AVAudioTime!) -> Void in
                print(NSString(string: "downMixer Tap"))
                do{
                    print("Downmixer Tap Format: "+self.downMixer.outputFormatForBus(0).description)//buffer.audioBufferList.debugDescription)

        })

//let's get the input audio format right as it is
let format = inputNode.inputFormatForBus(0)
//I initialize a 16KHz format I need:
let format16KHzMono = AVAudioFormat.init(commonFormat: AVAudioCommonFormat.PCMFormatInt16, sampleRate: 11050.0, channels: 1, interleaved: true)

//connect the nodes inside the engine:
//INPUT NODE --format-> downMixer --16Kformat--> mainMixer
//as you can see I m downsampling the default 44khz we get in the input to the 16Khz I want 
audioEngine.connect(inputNode, to: downMixer, format: format)//use default input format
audioEngine.connect(downMixer, to: audioEngine.outputNode, format: format16KHzMono)//use new audio format
//run the engine
audioEngine.prepare()
try! audioEngine.start()

I would recommend using an open framework such as EZAudio, instead, though.