Display blog posts from Wordpress to my Drupal site and filter it by taxonomy terms
This is a bit complicated. You'll need to fetch the data somehow from WordPress and make it Drupal data. Fortunately, there's the Feeds module that can help you getting data from your WordPress and transforming it into Drupal nodes. You'll need to configure the Feeds to also parse WordPress categories and create taxonomy terms from it.

I recommend you to read the Feeds documentation before start using it.