2.) Yes, however if there is a fractional exponent that you eliminate and that fractional exponent's denomator was even note that you will only get the positive part of that function. This is also not valid for inequalities.
4.) Yes, unless it makes one undefined.
5.) I don't know. I'm sorry. However I know that taking the common or natural log of both sides is legitamate as long as both sides are positive.
6.) No, as one side may be negative.
7.) I do not know. I am very sorry.
8.) I've never seen a case where this is necesscary so I do not know.
9.) View number 8.
10.) I do not think so as it could eliminate negative signs on only one side.
They can all be justified by proofs that I do not know myself.