Synthetic or Non Synthetic? What do the dealers usually use?

Zoren 370

Never trusted the stealership to do any work in my Z unless they will allow me to physically present while they do the job.

Given the fact that your oil is that low it doesn't matter whether you put in a synthetic or non-synthetic what is more important now is to top it up immediately to the required level otherwise suffer the consequences of a blown engine.

I personally use a synthetic oil. Never had my oil go down that much I do have an oil cooler and I drive the Z hard most of the time.