Bulk actions enhancement

The bulk action is not working as I expect. Or I am expecting too much or there is room for enhancement in it.
The problem: I want to move all my posts filed in one category to another category.
To do so I figured this steps: select all my post now filed under category Old_cat, add to them the category New_cat, remove the category Old_cat.
From the Posts page I can filter all the posts by one selected category, I did it choosing category Old_cat.
I can see 15 pages of posts, but if I select the checkbox Title I can only select the posts in the fist page.
So I have to select the posts in the 1st page, add the category New_cat, move to the 2nd page, select all the posts in it, add the New_cat, move to the 3rd and so on.
I’d like to select all the posts after applying a filter.

Moreover, if I filter for a category X, select a bunch of posts and then bulk edit them I expect to see the category X selected in the interface. and if I check a new category Y I expect to see the checkbox change from not selected to selected and this doesn’t happen.