Just wondering, why are the words written like "The old (the cities/towns) are interesting"?
We call this a double definite. It's one of the differences between Swedish and Danish, we do this but they don't. In phrases with adjectives like de gamla städerna ('the old cities') or den gamla staden ('the old city'), the noun needs to be in the definite form, and there needs to be a definite article in front (except in some names etc).
In English there is a difference between saying "The Old towns are interesting" as in particular old towns which are interesting; and "old towns are interesting" meaning all old towns - how do you capture this?
This sentence is the former. The latter would be "Gamla städer är intressanta."
Yes. There are some cases where expressions have become more or less names, where you can skip the article in determinate phrases with adjective + noun, but that's only in special combinations. One example of that is Vita huset 'The White House' which is a name and therefore is used without the article in Swedish.
"Gamla städerna" meaning is old town like f.e. Cracow or Oxford or part of the town which is old, have a church, town hall etc?
I'm still having difficulty with the, this, that, these, and those. How would these and those work in this sentence?