Recently active topics in Wordpress tagged with website

The only info about blogger and wordpress that I've found has stated that I either need to:
1. Customize my Blogger/Wordpress so that the blogging site looks like my site. or
2. Put the blog on a separate page of my own personal site.

What I really want to do is take the entries from the blogger site and place them in a small spot on my website's homepage. Can anyone help me?

How do I "retire" a WP site -- keep it online, but static. I don't want to have to update to new versions, but want it secure going forward as well.

What files need to be removed? Or is there an extension or 3rd party option for this?