My experiences are as follows.
When you ignore someone, you can't see their posts, but can they see yours?
Yes.
If they can see your posts, can they reply to them, it's just that you can't see them.
Yes.
How public is ignore information. Can other people see who you're ignoring?
Sometimes it's private, sometimes it's not. I would suggest public. Makes it more transparent, so people can see why the posts aren't responded to, and that it's because of ignoring rather then not having a response.
That being said, I much prefer not to have an ignore function. I hate it, quite frankly. Good moderation also should make ignoring stupid or trollish posters redundant, as they will be dealt with by the moderation staff.
I hunt for the truth
I am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead