Based on your screenshots, you should be adding these text elements to the map, not the layout. Have you looked at using a Graphics Layer in your map? This would allow you to drop text and points, etc., to your map. This ties your text to their place on the map.
The text size will scale up and down to always display at the font size you specify, but will anchor to the point you placed it. If you want the text to scale with the map (smaller as you zoom out), you'll need to establish a Reference Scale. Again, this is done on the map, not the layout.
Adding the text to the layout ties them to their position on the page, and ignore the map's scale and extent entirely.
Taking things a step further, you might consider using annotations. I've always found them to be more trouble than they're worth, but if you really want scale-specific, fixed text, they're the way to go.
- Josh Carlson
Kendall County GIS