As do fuel cells and H2 tanks - H2 is quite aggressive to the materials. But most importantly, the charge-discharge cycle of a battery is about 90% efficient, which beats hydrogen easily. And with quickly dropping battery prices they even become feasible for large-scale storage, see the Australian battery built by Tesla.
Depends on the li-ion. There are chemistries out there right now that are good for 20,000 cycles like LTO. And a substantial amount of li-ion research is extending cycle life.
It doesn't matter how good hydrogen becomes. Battery tech will continue to improve faster than hydrogen tech. H2 will never catch up.