My question is the following:
Does knot Floer homology detect the genus of null-homologous knot in rational homology spheres?
If the answer is yes, I would like to have a reference for the statement of the result and the proof.
Link Floer homology detects the Thurston norm, see this paper by Yi Ni.
EDIT: There are some lecture notes that Robert Lipshitz just put up on the arXiv, where he discusses the problem you're interested in. I haven't had time to look carefully into them, but he's usually very careful and clear in what he writes.