No, they are not always invalid. You just can't assume that they're always true. Think of this example: If you are happy, then you must be smart.

H->S

If you are smart, you could also be happy (MR). If you are not happy, you could be not-smart (MN). The whole point behind MR, MN and contrapostitives is that contrapositives MUST ALWAYS be true, but the others could be, but are not *necessarily* true.

Yes, the inverse and converse (Mistaken Negation and Mistaken Reversal in the Powerscore lexicon) are always invalid. Validity and truth are two different things. Validity occurs when your conclusion must be true based on the truth of its supporting premises. So here we have the affirmation that functions as our premise:

H-->S

And we can validly conclude two things:

1.) The affirmation itself H-->S, which is circular and essentially useless as a separate conclusion, but by definition valid;

2.) The contrapositive !S-->!H, as the truth of this statement is inferred from the truth of the premise.

The other two conclusions we can reach are invalid:

1.) The converse S-->H.

2.) The inverse !H-->!S.

The fact that our original affirmation H-->S is true but these latter two statements based on it could possibly be false is what makes them invalid. We don't need to prove a conclusion false to invalidate the argument, just that the possibility is there.

Either way, the inverse and converse may be true - we certainly cannot prove them false - but are invalid.