When teaching your language to a foreigner...

[meidei]

We call it Ancient/Classical and Modern Greek here, btw 
I believe "strong" compounds like the ones found in German are not common in the Modern language.
Modern Greek is quite periphrastic, unlike the Ancient language.
As you can see here, most terms are made of two words or more, even if they are shorter than the German equivalents
http://www.greek-language.gr/greekLang/ancient_greek/tools/structure/terms.html

[Misztina]

I'm a trainee English teacher so to say and all I can say that there are many things to consider.

The best is if you have the chance to learn in the target language's country or learn from someone whose mothertounge is English.
But usually, at least in my country in small towns we don't really get the chance to use these methods. I think watching foreign movies in their original language helps a lot, plus many visual things shoud be used, like pictures, role-playing etc.. It is always good to listen to songs and look at their lyrics. Sometimes it can surprise one.
Grammar should be taught too, because that gives you a better image. My friend says, who works in London, that she conciously avoids using "I ain't got no money." and says "I haven't got any money.", because she does not want to be looked down by others. That does not mean however that grammar is everything, but the basics should be there at least. Not that I am the one who is talking with all my typos and errors.

[mangaluva]

"Feel for language" sounds right.

Really? To me it's kind of clumsy. I wonder if this means that I have no Sprachgefühl for English...

It also sounds somewhat strange to me. I had simply created language feeling.

You'd generally say that "He has a good feel for the language". Saying "He's got good language feeling" just sounds... odd.

[Callid]

"Feel for language" sounds right.

Really? To me it's kind of clumsy. I wonder if this means that I have no Sprachgefühl for English...

It also sounds somewhat strange to me. I had simply created language feeling.

You'd generally say that "He has a good feel for the language". Saying "He's got good language feeling" just sounds... odd.

I had said: "His language feeling is good" or "He has a good language feeling" (without got).
Anyway, are there rules how to use "have got" instead of "has"? I'd only use it as a synonym to "possess".

[mangaluva]

"Feel for language" sounds right.

Really? To me it's kind of clumsy. I wonder if this means that I have no Sprachgefühl for English...

It also sounds somewhat strange to me. I had simply created language feeling.

You'd generally say that "He has a good feel for the language". Saying "He's got good language feeling" just sounds... odd.

I had said: "His language feeling is good" or "He has a good language feeling" (without got).
Anyway, are there rules how to use "have got" instead of "has"? I'd only use it as a synonym to "possess".

Again, those just sound undefinably off. Not wrong, but just not how you'd say it.

I think the different between "has" and "have got" is to do with tense and perspective; You'd use "have got" for first or second person, for example ("I have got" and "you have got" rather than "I has/you has"; you could also just say "I have"), but you'd use "has" for third person singular "he has/she has", but you wouldn't say "they has": it's "they have"). In future tense, you'd always use "have" ("I'll have/you'll have/he'll have/she'll have/they'll have").

[Umandsf]

Also, "has/have got" is grammatically incorrect. [shot]

[mangaluva]

Also, "has/have got" is grammatically incorrect. [shot]

Yes, but it's so widely used colloquially that frankly it just sounds odd if you don't use it.

[dilbertschalter]

Also, "has/have got" is grammatically incorrect. [shot]

How so? It's just a different tense (present perfect) and it's also required when you use a contraction.

[Umandsf]

I guess. I don't ever use it, so I could be wrong. Therefore, leaving out the "got" doesn't bother me at all. Probably it bothers me because I find it a little redundant, since "has" implies the person already possesses it, while "got" is a past tense word for receiving. Oh, well.