abouy git reset command

Hi, I just want to make sure whether my understanding of that command is correct or not. I have 3 basic requirements:

1. I have changed something after the commits and I think those are wrong.
So I want to undo all changes and the working directory should reflect last
commit:

git reset --hard HEAD

2. I have some changes in the index and I want undo them.

git reset HEAD

3. I just want to undo the last commit but not the working tree:

git reset HEAD^

If they are correct commands please let me know. 

Besides in the man page for git reset it is mentioned:

git-reset - Reset current HEAD to the specified state

Which means it is supposed to work with commits. But why is the same command work in case 2 and case 3 above?

Moreover, can any body tell me the use of

git reset --soft

The following language is confusing:

--soft

    Does not touch the index file nor the working tree at all, but requires
them to be in a good order.

Thanks in advance.