Also the "Palestine" side of the warrants are against Hamas which also feels weird (Hamas is also not a signatory nation and many suggest that Hamas != Palestine).
The ICC prosecutes individuals not states, so there's no contradiction here.
Given Palestine is a signatory does it mean they have to take action to extradite the Hamas leadership to face trial?
Yes
What consequences do they face if they fail to do that?
There's no penalties built into the statute. It tends to have diplomatic blowback. See [1] for a prior example.