1. ‘You can ask me anything’ translated as ‘tu peux me poser n’importe quelle question…’

That is not the only possibility; the plain possibility is just as valid, provided the context is right, and in fact it’s valid in two contexts.

a/ question asking

Tu peux me demander n’importe quoi. or Tu peut me poser n’importe quelle question.

b/ financial help (for instance)

Tu peux me demander n’importe quoi.

2. “quoi que ce soit” and “n’importe quoi” mean exactly the same thing.

   • Quoi que ce soit que vous ayez à dire vous ne pourrez pas la convaincre.
   • N’importe quoi que vous ayez à dire vous ne pourrez pas la convaincre.

3. “Tout” can be used instead of “quoi que ce soit” and “n’importe quoi” but in certain contexts only and it is slightly weaker in its insistence on the universality.

   • Tu peux me poser des questions sur tout, sur n’importe quoi.

difference

• Il sait tout. different from – Il sait n’importe quoi. (By the way, it is difficult to find a context for this latter sentence, which is nevertheless grammatically correct.)

• tout dire very different from -dire n’importe quoi

In the first of those two examples the signification is always “to say everything (about a given subject)”; in the second it is totally different: it is “to talk nonsense”.