I am using a TV as an external monitor, but the screen does not fit properly. Only the top half of the apps on the bottom dock are visible, and none of the top menus on the desktop are showing. On Windows 10, there is an option to "Fit to Screen" which resolves these display issues. Is there anything in Elementary OS that is similar?
Most TVs "overscan" by default, which cuts of the edges of the picture.
You'll want to turn this off in the settings of your TV. Oftentimes you'll find a button on the remote or a setting in the "Picture" settings on your TV to change the size or overscan settings of the output.
For example, you might be able to switch from 16x9 to Screen fit, or something similar depending on the TV brand.
Have you tried setting the external monitor as the primary? You can do this by "starring" it in the Displays settings.
I had pretty much the same problem with display on an external monitor - display was fitted badly; I hardly could see wingpanel or plank.
I solved it with changing config file in /boot/ directory.
In this file you need to find disable_overscan and change it's value to 1. Then a bit further down you'll find
overscan_bottom=48 overscan_left=48 overscan_right=48 overscan_top=48 you can change these values to fit your display into monitor.
Then save it and restart computer. It should be fine after few times. :)