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1) If not, will hurt the keywords PR?（i mean PR not focus something, i am a newbie, dont know how exactly express this situation）

2) Then I post a new article, the article will show on the home page (at least the title of the article will show on home page).So the keyword in this title counted in home page or counted in category page or counted in the article page?

3) If i have set the "Use noindex for Categories", I don't need to consider the keywords PR problem on category page, do I?

1. ...What? If not what exactley? Your title is confusing as hell!

2. Keywords apppear wherever they are on a page that is indexed.

3. noindex *should* not appear using a noindex policy, but its not always perfect, and whatever structure you are using for your site (i assume wordpress by your question), where your theme may be inserting references to new or old content (blog page, archive page, breadcrumbs etc), and what meta information you have wordpress set to use.