You use nach without the article, hence nach Deutschland but in die Schweiz, since you use Deutschland without, but Schweiz with the definite article. On the other hand, a non-proper noun with zu as a directive adjunct or complement is always used with an article.Are "nach" and "zum" interchangeable in above context?
The rule concerning countries is: if it's a neuter noun used without article, it's "nach". If it's a masculine or feminine country used with article (e. g. der Irak, der Iran, der Libanon, die Türkei), or even a plural, like "die Arabischen Emirate" or "die Vereinigten Staaten", you use "in" with accusative and you don't omit the article.No, "nach Hause gehen" is a fixed phrase, you can't use zu with it. And you can't use "nach" instead of "zum" here, either. You could use "nach" if it were followed by a city or country ("nach Berlin," for example). By this logic, your home is kind of seen as a city or country itself, while if you went to someone else's house, it'd be "Zur Fanny (Ich gehe zu Fannys Haus)."
Sometimes you can even use "in". "Wohin geht denn die Reise?" "Ins Weltall!" (not very likely, but you know) or "In die Karibik."
In contrast, with a country it'd be "Nach Griechenland" and if it's a...I don't know, an object of sorts, it'd be "Zur Großen Mauer," for example.
Also, I have never in my life heard someone say "Wohin gehest du?", it's always "Wohin gehst du?" Just wanted to clarify that because you might get a few weird looks if you said "Wohin gehest du?" anywhere other than on a stage or something.