You can be an engineer without an engineering license. Safety-critical jobs usually require a professional engineering license, but there are a lot of engineering work which is not safety-critical.
When it comes to civil stuff (i.e. the safety critical thing people think of when they hear engineer - bridges, buildings, highways, flood protection...) you absolutely can't call yourself an engineer without professional accreditation in every jurisdiction I know.
Even then (buildings for example), I believe some of the work can be done by non-licensed engineers. Stuff like land surveying, some electrical, CAD/modelling work, design of plumbing, heating, etc. can be done without license. I know a few people that aren't licensed but work on condos as engineers. I'm guessing a lot of the stuff has to be reviewed/approved by a licensed engineer, but that could be 1 to 5 licensed:unlicensed for example.
An engineering graduate, or an engineer-in-training. You can call yourself an engineer once you have several years of experience, pass some exams on law and ethics and whatnot, and get a professional designation.
That is downright ridiculous, sorry. You are an engineer, just not a "certified" or "accredited" one for some sub-set of tasks/things/requirements. The fact that we have to even discuss this as if saying you're an engineer is some ultra-taboo because people might "mistakenly" allow you to do mission critical or potentially dangerous work without asking for your specific accreditation is disturbing and Orwellian-like policing of plain language.
There's only one state in Australia that has mandatory registration of engineers. There are several more states that are currently starting up mandatory registration schemes, and of course the national professional bodies operate voluntary registration and accreditation schemes.
Now of course that doesn't mean that you can just start building bridges as a non-accredited engineer, I expect the courts would look unkindly on you in a negligence lawsuit if your company had engineers that couldn't demonstrate their professional qualifications and development.
This is seen as a problem and the professional bodies are pushing more states to adopt mandatory registration, so we'll see more of that in the next few years, but it's not like Australia is a land where bridges fall down weekly without mandatory registration.