Problem with custom post type

Hy guyz

I have some problem with Custom post type

I create custom post type board games and taxonomies languages, authors and type. Languages and authors are just like post tags and type is category in posts.
And now I have some problem:

1) How can I create in theme that when I open some board game just like in post “posted in ….(category)” but here I want “posted in … (type)”, and when I will click on some type, it will show all board games who are under this type.
2) now when i click on some post category (Uncategorized), the search show me all post and board games an not just post which are Uncategorized

I have some more problems but first i want to fix this 🙂