Am I able to go and live with my Chinese girlfriend in China for a year or two?

If you will work in your company branch in China, you can apply for a work visa. Otherwise, you can apply for a tourist L visa. Please keep in mind that since you are not married, you can not get a visa good for one year or two. And you are not eligible to get a temporary residence permit if enter with an L. This permit is for work or student visa holders, or long term family visitors.

My company does not have a branch in China. I will do all my work online.

Is a tourist visa really the only option?
How long can I stay as a tourist?
How many times a year can I get it?
Do I need to leave China before I can apply for a new one?

yes, you can only get a tourist visa, generally, it allows 30 days stay. You can extended it twice with 30 days each. So, 90 days in total. You can apply it as you like without limit. For NZ passport holder, it is possible for you to get in HK.