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I know of German separable prefix verbs and of English phrasal verbs, but these examples seem to be of phrasal verbs on German that do not fall under the definition of separable prefix verbs:
What category do such verbs belong to?
Are they used similarly to separable prefix verbs?
There are two different but similar things.
Regarding weg sein see also my answer to the question “Der Berg ist hoch.” Adjektiv oder Adverb?.
The verb sein is the copula which links the subject to the predicate.
Ich bin weg.
Ich bin unterwegs.
Der Apfel ist auf dem Tisch.
Lassen, however, is used in a similar way to modal verbs. Compare:
Die Mutter lässt die Kinder fernsehen.
Die Kinder dürfen fernsehen.
This is a complex predicate (mehrteiliges Prädikat) and the verb lassen forms the predicate of a sentence together with the infinitive of a full verb.
