Is there a way to show the latest/new forum posts? Something that can configure the number of topics to list at the very least. I would love a block that ban be placed at the top of my forums or in a new page dedicated to new topics. None of the blocks I have will allow me to do this. 

Look at creating a stream. 

One of the default out of the box streams is just unread content.  On this site an example is: 

https://invisioncommunity.com/discover/unread/

You can customize this to show only specific forums, show all content, content you started, content you participated in, etc. There are lots of ways to slice and dice the data. 

You can define new default streams in your AdminCP. 

5 hours ago, Ford Doctor said:

 None of the blocks I have will allow me to do this. 

What’s wrong with the Topic Feed / Post Feed blocks?

You can add topic feeds as mentioned above

https://invisioncommunity.com/4guides/getting-started/using-the-block-manager-r309/

Then you also have streams

https://invisioncommunity.com/4guides/how-to-use-ips-community-suite/content-discovery/activity-streams-r69/

With streams you can set up whatever you need for your users, and users can actually create their own too