php include problem

Why don't you just rename the html file with a php extension?

Try this also...

You have
<div id="Layer60"><?php include('../../meniu-principal.html'); ?></div>

make it:
<div id="Layer60"><?php include("../../meniu-principal.html"); ?></div>

Single quotes from my understanding are used to display a literal. Because you are trying to include a page I would think you want to use double quotes.

No, include(../../file.html) isn't valid either. Syntactically, include() is just a function to which you pass the path to the include, as a string. Strings must always be wrapped in quotation marks (PHP does make an exception for undefined constants, but you shouldn't rely upon it).

According to these errors you're doing include('f1/f2/meniu-principal.php'), not include('../../file.html').

Single quotes are used to express a literal string — no special operations will be performed on it, like escape code interpretation or variable interpolation. "$a\n" contains the value of the variable $a followed by a newline, but '$a\n' contains a dollar sign, the letter 'a', a backslash, and the letter 'n'. It's faster, so it should be used where no fancy stuff is required.

You should also note that your site's code breaks an awful lot of good Web development practices.

can be the problem that the version of php that hosting company uses is older?

No. PHP has supported include() pretty much forever.