Can anyone call himself an engineer?

You can attend numerous training classes everywhere that last as little as a week and you will get a certificate that states you are a "engineer" in that subject at the end of it.

Sure.  Last week I cudnt even spell enganere.  Now I are one.

Yes.

No/Yes.

Yes.

only is you have a degree or trade papers . by the way , what type , electrical , mechanical engineer , soil engineer .

Yes, anyone could call himself an Engineer but calling yourself one and being hired as one are two different things.

In the US, you can call yourself an engineer if you're working as an engineer. People who say "engineer is a protected title" are kind of confused about the reality of the engineering industry. Just don't call yourself a Professional Engineer (capitalized).

In the US it varies from state to state. Where I live you can not call yourself an engineer unless you are a registered professional engineer. 

It is not a protected title in the UK and I think not in the USA either. I think it is a title in Germany and after that I have no idea. 

In fact the word has become almost meaningless in the UK/USA with contract engineers etc. and a garbage man is often described as a sanitation engineer. No disrespect to garbage men but they did not go to university for 3+ years studying one of the most time consuming and difficult subjects. 

And as an Electronics Engineer I am used to people interpreting that to mean I am an electrician who does house wiring.The protected title in the UK is Chartered Engineer. Although from my understanding of what being "Chartered" entails, then it actually means "Person in charge of work done by actual engineers but who is in fact no longer an"

Expanding on Bill's answer (still U.S.)

There's a formal "Professional Engineer" title, which is licensed at the state level.

Some work requires that a licensed P.E. signs off on it.  This applies mostly to structures and large mechanical / industrial systems, where failure can have life safety consequences.

Ordinary engineering is not so regulated.

depends on the country.

US, no it is not protected. If someone will hire you, you can work as an engineer without a degree.