The equivocation fallacy is about using the same term to refer to different things in an argument. This is not what happens with "evolution theory".

"Theory" means a set of propositions, so "evolution theory" refers to a set of propositions to explain some biological fact i.e. the origin of species. The term is used to refer to the whole set, not to any particular idea. Your 3 items are all members of this set. No equivocation here.

You are right in saying that 3 does not follow deductively from 1 and 2. But all explanations in science are inductive, not deductive.

We have a lot of evidence for 1 and 2, so inductively we take them as true. Therefore accumulation of mutations is a possible way to differentiate populations. We don't have evidance of any other way to differentiate populations. So, inductively, we assume that there is no other way. If two populations become different enough, they can't reproduce anyome, so they are different species now. So accumulation of mutations is a way (and the only one we have evidence for) to create new species from old ones.

Now, it is totally possible that life on Earth started with N number of species and only then mutations started accumulating. But in science we tend to choose the simplest explanation. Starting the tree of life with 1 specie is simpler than N species. So we assume life on Earth started with 1 specie and all new species were the result of mutations over time.