How to identify a phrasal verb + object from a verb + prepositional phrase

If the particle cannot be an adverb, it must be a preposition. An example: "from" cannot be an adverb. So when a verb is used with "from", the "from" must be a preposition. That settles your "fell from" example: "from her bicycle" is a preposition-phrase.

Failing that, one way to tell the difference is to try using a pronoun as a direct object. If the particle is an adverb, the direct-object pronoun must go between the verb and the adverb-particle.

Adapting your Example 1:

Example 1a: She's always talking about them

Example 1b: *She's always talking them about

1b fails, so "about" in this sentence can't be an adverb; it must be a preposition. So "about them" is a preposition-phrase. By contrast, with regard to a misbehaving child and her toys,

Example 3a: *She's always throwing about them

Example 3b: She's always throwing them about

3a fails, so "about" in this sentence can't be a preposition; it must be an adverb. So the verb is "throw [something] about".