Change Taxonomy Permalinks

If not, can i just override default taxonomy URLs to point they to my archive-page?

I am not sure about newer version of the WP, but In the past I managed to create a taxonomy, say ivan_taxonomy and I also created a page, which slug was also ivan_taxonomy. So, when user viewed posts through example.com/ivan_taxonomy/super-cool-post/, he could have gotten easily to example.com/ivan_taxonomy/ and my page was being displayed. (Not sure, whether you wanted to know sth like this :-D)

And I want something like this:

…

Easy, grab a url param and create a WP_Query with dependence on it, for example:

if(isset($_GET) && false != $_GET)
{
    //whitelist
    $allowed = array("category", "tag");

    $url_params = array_keys($_GET);

    //get your term, provided it is the first in a query, 
    $term = (string)array_shift($url_params);

    //get your id
    $id = (int)$_GET[$term];

    //validate input
    if(in_array($term, $allowed) && (false != get_the_term_list( $id, $term )))
    {
        $query = new WP_Query(array($term => $id));
    }

}

Or it would be a lot easier with url like example.com/archive-page/?term=category&id=8.