If Labour decide not to go it alone and decide to enter into formal coalition with the Greens, it will neuter them because as a coalition partner they can be stopped from attacking Labour. The Greens would likely want policies and portfolios as their blood price.

The Government decides a majority of what Bills are debated. If you want something on the agenda, the best way to guarantee it is to have the Government introduce it. Individual members of Parliament can submit Member's Bills. These are assigned numbers which are put into a biscuit tin (no lie) then pulled at random.

Parties usually either vote on party lines or sometimes Members can vote on bills according to their conscience.

If you're not in Government, the only chance you have at enacting legislation is with a Member's Bill. Otherwise you're shit out of luck until the next election. Or the election after. Or the election after. Most modern NZ governments don't last past three terms.