Learn English – Does “Three countries including Germany, Canada, and China” sound unnatural

The two sentences you give are the normal way to say this.

The other common way to express this idea is to say, "The foreign countries that I have been to are Germany, Canada, and China." Putting "three" in there would be awkward. But it would flow naturally if you're emphasizing that this is a small number, like, "The only three foreign countries that I have been to ..."

Using "including" would be wrong because "including" is used when you are giving a partial list, not a complete list. You could say, "I have been to three foreign countries, including Germany." But if you list all three, than it's not "including" any more. It's the whole list.

"Containing" is used when the things listed are stored in some bigger thing. Like, "I have a closet in my bedroom containing my clothes and my shoes." It's rarely used to talk about countries because we don't normally think of countries as being inside something. Perhaps you could say, "Europe contains Germany and France", but I don't recall ever hearing someone say that. People do talk about "containing" a country when they mean to restrain it in some way, like "During the war the British navy kept Germany contained on the continent."

"Consisting of" and "comprising" are valid if you talk about the countries you have visited as a list. That is, you can't say, "I have visited three countries consisting of Germany, Canada, and China", because there's no object there to do the consisting. You could say, "Here is a list of countries I have visited, consisting of Germany, Canada, and China." But that seems an awkward way to express the idea.

Why don't you want to use a colon or the word "namely"?