Is this a sidebar?

The website in question is https://www.altadenabaptist.org/wordpress/ and I’m trying to get a plugin, such as wp-dtree-30 to work. I’ve tried several and just can’t seem to get anywhere. And yes, I know I need to update from 2.3.1 but I’ve updated a few times while working on this problem and am not doing it again til it works. I’m wondering if my understanding of what a sidebar is correct. The part that says
Archives
* January 2008
* December 2007
* November 2007
is what I’m trying to tidy up so that it’s like
Archives
* 2008
* 2007
* 2006
with being able to expand a particular year, and maybe that isn’t really a sidebar?

I’ve made some screen captures here to help with my question: https://www.altadenabaptist.org/problems/sidebar1.html
1) you can see that I do have wp-dtree-30 activated.
2) shows the template, which has minor modifications to the WordPress Default.
3) shows that the sidebar widget seems to be working
4) shows the theme files. Note that there are two archives, though I don’t know why, and which is the actual one being used.

So, is the part on the side actually what is meant by a sidebar? If so, then why won’t any of the widgets I’ve tried work? Help, I’m going nuts!