Open a APP in a specific monitor

One other thing to note, is that you must have a minimum

of two Desktops available on the second display (three is better

if you already have an app open on that display). I believe part

of that may be due to the possibility of apps in full screen mode.

I saw something right-click show options to open in a specific desktop, but for me, this option doesn't appear.

In Mission Control System Preferences, do you have Displays have separate spaces selected? That is the only way to treat the two monitors independently. If you have it unchecked, then the two monitors are a single display and there is no way to separate the two.

If you don't want them as separate displays, an App should open its windows in the same place the last window was closed, but that is entirely app-dependent.

The solution Barney indicated is fine, and works if you always want an application in a specific display.

There is also an option to open an application in a specific display at some point in time, without assigning it in the Dock.

Click on an empty area of the menu bar on the display you want, then start the application via Spotlight.

For example, say I wanted to start Safari on my external display:

1) Click on the menu bar on the external

2) Press command-space to open Spotlight

3) Type, e.g., Saf and press enter

Generally the best idea is to move that App's window not maximized over to the monitor in question before maximizing it. That way it stays on that monitor.