For example, how would you say translate/reformulate the sentences in a way that sounds natural in German?
I think the present participle doesn't work in these cases like it does in English, does it? I tried to find examples online but it's difficult to find a general explanation of how one would make such sentences in German.
I think your two English examples are fundamentally different and do not fall into the same category. He was seen doing something means that someone was observed doing it, while he can be seen doing something means that he does it.
I saw John eating means no more and no less than that the speaker saw John eating. In German, you might say something like Ich sah John essen. Simple as that.
They can often be seen roaming through the mountains, though, doesn't mean that "they" are necessarily often observed roaming, just that they roam often, and could potentially be seen doing it if someone actually looked. To express the same meaning, in German, you might say something like
or any other phrase that expresses that someone does something regularly.
I saw John eating. — Ich sah John essen.
Sehen is a verb of perception and those can take an infinitive in German. They are very similar to modal verbs in other regards as well.
They can often be seen roaming through the mountains. — Sie können oft beim Durchstreifen der Berge gesehen werden.
This example is a bit tricky because of that extra piece through the mountains. In German beim Durchstreifen der Berge is one huge modal adverbial that even incorporates the preposition through as a verbal prefix durch. The extra preposition bei marks it as a modal adverbial.
If you left that part out
They can often be seen roaming. — Sie können oft stromern gesehen werden.
becomes an alternative. Though beim Stromern is more common.
