Question: I have read some time ago that [z] is the voiced counterpart of [s], as [d]-[t], [g]-[k], [b]-[p] and [v]-[f]. For all pairs except the first, I was able to consciously perceive it by starting to pronounce the unvoiced consonant, adding voice and realizing that I am now doing a voiced consonant.

However, when I start to produce a S (AFAIK a hissing sound) and add voice, I don't get a Z, but rather a hissed Z. AFAIK Z is the same sound a flying insect (eg bee) does and has no hiss on it. Or is that another phone? Am I the only one who perceives this difference between a voiced S and Z? I don't know if I'm mispronouncing [s] or [z], somehow affected by my native language (Brazilian Portuguese) or by some regionalism.

Answer: 
Phonetically, the only distinction between a pure, unaltered IPA `[s]` and a pure, unaltered IPA `[z]` is voicing. However, most languages don't use pure, unaltered IPA `[s]` and `[z]`!

One phoneticist I know, for example, tends to pronounce English `/s/` as `[s͎]`: a "whistled" sibilant with a very distinctive, high-pitched "overtone". This makes his `/s/` very different from his `/z/`, in more ways than simple voicing.

I can't say for sure without a recording, but your `/s/` may be similar, or have some other feature setting it apart from `[s]`. If you want to make sure, I'd suggest finding some good phonetic recordings (the ones made by Ladefoged are especially famous) and comparing your `/s/` against them.
the voiced [z] requires a harmonic vibration to create a low frequency oscilation to modulate the voice and is, in my case, liable to fricate with as much of the tongue as possible. The voiceless [s] is just a noisy turbulence; any added voice is not necessarily harmonically modulated and the place of articulation may differ slightly, if only the tip of the tongue touches the alveolar ridge from below, or the dents.

The exact forming of the tongue can differ for channelling the air stream(s) differently in either case and not necessarily in the same manner.

To my surprise, closed teeth aren't needed to produce the sounds, although the vibration between the teeth is needed for me to satisfy the feeling that I fully formed the phoneme. There is a strong prejudice against lisping in German, which might somehow explain that (I think I recall being called to order exactly once), quite different from thSpanish. German also lost *th*, which Proto-Germanic presumably had.