§22

In this passage Wittgenstein wants to undermine Frege's view "...that every assertion contains an assumption which is the thing that is asserted". I don't know whether this is an accurate portrayal of Frege's view - which of Frege's works is he referring to here?

I think Frege's view (or Frege's view according to Wittgenstein) is this:
That different kinds of sentence contain the same content but differ in terms of the 'force-operator'. The 'assumption' in question is an unasserted proposition (is that right? - proposition?). So you could take a proposition like 'there are twelve chairs in this room' and simply contemplate it without asserting it - or you might assert it - or you might ask whether there are twelve chairs in the room. All three cases share 'there are twelve chairs in this room' in common but you might 'add' assertoric force or you might add interrogative force (make it into a question).

Wittgenstein thinks that it is mistaken to think of an assertion as consisting of two acts - (i) entertaining (e.g. entertaining the proposition that 'there are twelve chairs in the room) and (ii) asserting. For one thing, Wittgenstein says, we could write every assertion in the form of a question followed by 'yes' or 'no' but this would not demonstrate that every assertion contains a question.
Wittgenstein's point here - I think - is that assertions are not the primary or prototypical components of language. If we want to understand language and meaning it is important to think about questions, commands, assertions, cracking jokes, and so on - all of the various language games.

Philosophers of language are mistaken to focus on propositions/assertions - including Wittgenstein himself in his earlier work. Language is made up of diverse 'tools'.