Please help: buffer (carbonate hardness) is 0!!!

I've just setup a new aquarium (29 gl, flourite and a few plants, 55W
CF). My water tests look a little wierd: the carbonate hardness is 0,
while total hardness is 120 with pH 6.8 or 7 (I can't decide which
color fits better). So, I assume, that the only hardness I have is
non-carbonate.

1. Does non-carbonate hardness contribute to buffereing against pH
fluctuations?

2. Is it even possible to have 0 alkalinity?

I am afraid to introduce fish until the water is fully conditioned.
I've checked the local stores for buffer increase - all chemicals
concentrate on adjusting pH, while I am quite happy wih mine: I would
like to keep tetras, danios, loaches, ottos (and/or) and live plants.

3. Can you recomend what exactly I should be looking for?

4. My chlorine measured .5 (no chloramine) Is it safe? Should I
dechlorinize?

5. All dechlorinizers that I see also try to take care of nitrates,
ammonia, etc. I would love to have a bio filter established and
control those by balance, not by cheistry. Should I use it anyway to
should I keep looking for something specific for chlorine (if it
exists)?

6. If I have so much non-carbonate hardness, it is probably sulfate or
phosphate. Should I control those? I am conserned that since I have
very few plants, it is going to promote algae growth (my tap water
initially comes with nitrates 20)

Please help! Thanks in advance,
Elly