Detection of Microwave

I would like to know how to detect microwave modulation at low frequency and I would like to know measure it

You don't say what frequency, low is not much help.
PIN diodes are often used, a quick search using "microwave modulation detection using diode" yielded some results.
If you are talking the low end of the microwave spectrum, there are a number of Integrated circuits that will do the job, the LTC5564H is an example.
Cheers,
Richard

PIN diodes are used to create amplitude modulation (and for switching), but are useless to measure it. For that you want a detector diode, or as pointed out, any of a number of ICs that can strip LF modulation off of a microwave carrier. Analog Devices, Maxim, and Linear Tech all make these.

I understand that we can only detect microwave using devices .

Any hand portable device that we can detect microwave modulation at low frequency ?
Anything that we can see the heat from microwave around us using software or other tool ?

I am looking for detection microwave at low frequency 0 to 100 Hz , and I am looking also for visualization of microwave around us ?

It sounds like you're looking for a field strength meter. Narda Microwave, lessemf.com, and a bunch of other people offer them, and I'm sure you can find low cost options in ham radio publications. You probably want a broadband rather than tuned design. Unless your field strength is really low you could probably make adequate qualitative measurements by cobbling up a microwave version of a crystal radio - just a single turn loop with a microwave schottky diode between the ends, and an RC filter across the diode into a headphone amplifier to listen to the modulation. Of course, your ears don't go down to zero hertz, so you'll want a meter for the DC component. Google up "microwave field strength meter plans" for more elaborate schematics.

I got the sound signature file. It is really strange and cant figure it

Listened to the sound file, but with zero information on what it is you are listening to I can only make one guess. This sounds like the switching harmonics of a microcontroller executing a control loop. every time a button is pressed or some other event is processed it goes into the appropriate subroutines and returns. This shows up as the momentary noise changes. The rest of the time the loop just goes round and round waiting for something to happen. Am I right or even close?