Yes, the problem for the plants is most likely the low hardness / lack of nutrients. The water comes from a reservoir in Yosemite and is very pure, so I guess it requires a little extra work. My current gravel is fine grained (~2mm) so maybe that doesn't help either. =)
Unfortunately, experimenting with water parameters may have bothered my fish (he's kinda sick now). So in the future, I don't want to do any water parameter messing in my fish's tank. For that one, I want to be able to run it on tap water + conditioner with as little interference as possible.
To sum up: tap water sucks for plants. Messing with water sucks for fish. Solution: tank for fish with just enough floating plants to avoid a cycle OR cycled tank with no live plants at all. Question: given the small 5g size, which is more likely to succeed? Sounds like people have managed both ways. =)
Thanks for all the help, everyone!