Hello!
After my previous embarassment in misunderstanding the meaning of the running modes names, I decided to use my Uno as FDTI controller to check if everything is OK with the ESP (running it in normal mode, with GPIO0 high).
Well, now I can "hear" the ESP using a serial monitor when it boots up (I'm using Termite; see boot message below) with the Baud Rate of 19200.
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Ai-Thinker Technologyðg.
ready
But after that I'm unable to get inteligible responses from AT tests... I only get "garbage", suggesting the baud rate is wrong. But I tried all the rates, and none of them give me a response that I could understand. (tried "AT" and "AT+GMR").
Also tried to flash a new firmware using the ESP DOWNLOAD TOOL, but got "chip sync response" every try... double and triple checked the GPIO0 on low, and the flash set-up (crystal frequency, QIO, Flash size, etc...).
Is this supposed to be that complicated, or I'm unlucky? Every step I try to make give me a different problem.
Have any of you had a similar experience? 
*** UPDATE ***
Apparently it was a "luck" issue. I've got another ESP, and now it's fine.
Thank you!