I have set the number of posts to appear as 6 on my homepage. All posts appear with excerpts.
However, when a particular category is clicked, the number of posts showing is also 6. What I want is to show ALL posts when a particular category is chosen. I am OK to use a plugin like WP-PageNavi if required.

Can someone help ?

You might be able to use the List Category Posts or the Post per Cat plugin.

I use http://wordpress.org/extend/plugins/post-types-order/ to order my posts for all my projects - you could also try that.