I don't see what you mean when you see that creationists define information deliberately so that it cannot be increased through random mutations. The definition of information that they use, at least from what I have read, is the same definition given by information science.
Not usually. Can you give an example?
The changing of a bird's beak or wing-shape, to make it more apt at doing one thing may be beneficial, but it does not require any new information, and thus cannot be used as an example of evolution.
Of course it can be used as an example of evolution, since it is a heritable change in a lineage (I presume that when you say
a bird, you are not speaking literally; and would adivse you to cultivate a habit of precision.)
The new information needed by evolution can only come by incremental steps, and there is no example whatsoever of any new information being added to DNA that benefits it.
In order to say that, you would need to say how you're quantifying information and determining whether it's "new". This is usually where creationists fall down.
Even if you say that evolution does not require an increase in complexity, but can also be characterized by a decrease, that still doesn't explain how the increase occurs by means of that same evolution.
Well, given the range of mutations we know to occur, substitution, insertion, deletion, fission and fusion of chromosomes, etc, it is manifestly the case that there is a sequence of mutations (indeed, an infinite number of such sequences) that would get you from any genome to any other --- from a monkey to a man, or a frog to a fish, or whatever. Whether this would involve "new information" I cannot say, since creationists are infuriatingly vague about what they mean by that --- but it is certain that this is all that is required for evolution to have taken place.