When should this community wiki button be ticked while answering or edit?
When should I make my answers Community Wiki?
When you want to enhance the "wiki" aspect of your post, so that it can be a continually evolving source of good information through repeated editing.
When you feel your post would benefit from less concern about voting affecting the reputation of those participating in it.
Basically, when you want the post to be a collaborative one. Creating a CW post basically invites radical changes and additions -- unlike normal posts, where the wiki aspect is more in grammar/formatting/small tweaks.
The CW scheme is just when you want other users to help in revision of your post. Not for formatting,etc. which is already done by the fellow users - but, for improving (additional information) of your post which shouldn't be normally done by fellow users. They can edit the post for clarification. But, they can't change the post by adding additional info. There's also this historical lock (which a mod can put on a post) for the prevention of edit wars...
The influences: When a post goes beyond 10 edits, it's automatically reverted to a CW. When the post is marked by CW, additional (+) or (-) votes doesn't influence your precious reputation. Be sure to check out the -1'd user..! Well, he's the -1 in every site. He owns the CWs...
If you've got some time, consider reading What are "Community Wiki" posts? and When to mark the 'community wiki' checkbox on a new question? which are themselves CWs...