majinjoko:
Please forgive my inaccurancy, I'm quite a newbie on this field.
No problem. And correct me if my language is confusing 
majinjoko:
I understand your concern about the high power consumption of the wifi chip, but in a realistic scenario the wifi chip will be on&connected for 15-20 seconds per day. I made a lot of work on the software side to keep its usage at minimum. In any other case, the wifi chip will be completely off.
It's not a concern so much as a design point. For the reasons I discussed.
majinjoko:
If I understand what you wrote, I should use the dc-dc converter I already own (LM2596S) to handle the power coming from the battery.. but now, what type of battery do you suggest I use? Should I use 4 AA batteries?
Only you can determine if you "should" use your LM2596S. And as for what battery to use -- there are so many variables -- too many for me to make a determination. Plus, probably some calculus. I donno, if you want simple, with ease of replacement, then 4 AA Alkalines might do the trick -- but is there vibration involved -- that could, say, cause them to fly out of the holder? And, how often are you willing to replace them, etc? Then there's power demand... see if you can determine the peak current demand of the NodeMCU Amica [as per your application], then have a look at a datasheet for different batteries, and see if it/they can deliver that peak current. Also power to weight may be a factor, or power to volume, or all three, or ventilation, or ??? Also, if you DO use a DC-to-DC converter, then you'll need to factor in how that changes the current demands from the battery. And what about ambient temperature -- or the effect of a confined space? And primary, or secondary .. and if secondary, then there's the issue of charging the batteries. [But, I'm guessing primary, right?]
In other words, it's a HUGE subject!
majinjoko:
I am not able to find the Nodemcu datasheet, so I am not sure what is the correct voltage to apply to Vin.
Yeah, when I was Googling that, I noticed a lot of confusion on that subject. But, I did some more Googling and it appears that "NodeMCU" is the designation of some form of firmware running on the thing, and the module is an ESP-12e. If that's true, then Google ESP-12e datasheet, and you will, likely, find something pertinent.