Change Category Base For Custom Post Type or Posts Page

When you register your post type, in your options array, set 

'rewrite' => array( 
    'with_front'    => false 
),

this will remove the “blog” from the front. Remember to flush your permalinks after you make this change.

Not sure about categories being programmed through wordpress (it COULD be possible) but you could do a rewrite rule in your htaccess that redirects all /blog/category to /gallery/category pretty easily. Something like:

RewriteEngine On    # Turn on the rewriting engine
RewriteRule    ^/blog/category/([A-Za-z0-9-]+)/?$    /gallery/category/$1    [NC,L]    # Handle requests for "blog prefix"

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