I can no longer find the "arrangement" tab to click mirror display.

You can toggle mirroring on and off with the keyboard: command-F1 is the shortcut. Much easier than going to System Preferences :-)

Also, the Arrangement button only appears on one of the displays when mirroring is off. If you are looking at the System Preferences->Displays window on the other display, it is not there [Note: which display shows this is determined by the position of the white "menu bar".

Here is what I see in each of the two windows in my rMBP, with a second display (provided by an iMac in target display mode):

rMBP

iMac:

In the Arrangement area, see how the white menu bar appears on the rMBP screen:

So your mac is not recognizing that there is a second display attached.

How is it connected? Through an adapter - which? Through a usb dock with hdmi or display port connections?

Does disconnecting and reconnecting cables do anything?

Did you try holding down the option key, with System Preferences->Displays open, and clicking on "Detect Displays" (yes, this button does not even appear unless you hold the option key).

What version of the MBP?

You may also run Etrecheck and post its report here, so we can look for possible software conflicts.

You should run it again and follow the instructions for removing the adware that it detected.

I don't think that this is involved in the original problem, though.

You say "DisplayPort", but please be more specific. Your mac has a miniDisplayPort connection, and the Dell probably has full sized DisplayPort plug. You need some kind of adapter in between. It is important to know what - if it is just a cable with the different type of connectors at each end, or if it goes through a "dock" or something.

Also, if possible, try another cable if you haven't already.