Are "They are called living things.", "Those are called living things." and "Them are called living things." interchangeable? Do all sentences convey the same meaning?
They're not quite the same, and one of them is incorrect.
They: the things we were referring to earlier. For example,
My aunt and uncle live in Brixton. They have a big house.
So you might say, "These things are (whatever). They are called living things."
Those: the plural of that. We use it when referring to specific things that are farther away or more removed from our observation or discussion. For example,
These trees here are apple trees. The ones down in the valley? Those are pear trees.
So you might use "those" like, "These are rocks. They are not living things. But there are also animals. Those are called living things."
Them: Incorrect in this case. It's the object version of the pronoun they. You would use it like
My aunt and uncle live in Brixton. I went to visit them.
You can't say them are, because you need a subject there, not an object.
Your third sentence is not grammatically correct. Them is never used as a subject. This personal pronoun is used as an object (the same for her, him, me).
So, let's look at your first two sentences. If you are referring to the same group of things, the two sentences could mean the same but are conveyed differently.
They are called living things
This sentence could be in response to a question: What is that? They are called living things. If you are not referring to the same group of things, this sentence conveys a more general answer. The group of things is of unknown size and could be a larger population than the second sentence.
Those are called living things.
You could answer the same question with this answer, making the meaning the same. What is that? Those are called living things. However, if it is not the same group of things, this sentence conveys a more specific meaning. Those refers to a certain group of things, instead of the more general they.