As your partner has a temporary work visa, with the proof of partnership you say you already have, you would be eligible for a partner-sponsored temporary work visa to run for the same length of time as his.
With you doing casual work in a non-skilled role, there is no guarantee at all that you could get a work visa in your own right. It would depend on the employer showing that there were no NZers available to do the job, and that they'd tried advertising for them, and why anyone who answered wasn't as suitable as you.
One is a good probability, two is pretty unlikely and difficult.
Applications that are refused because a person doesn't meet the regulations at that time don't affect later applications - after all people's circumstances change so that later, they DO meet the regulations. It's fraudulent applications, or visas revoked for a criminal reason, that affect anything that comes after.