displaymacosmenu bar
The Mavericks feature "Displays have separate spaces" is nice except for one thing: With vertically arranged displays, you need to aim for the menu bar in the lower display.
This breaks the primary advantage of having the menu bar on the top of the display, which is that one can just throw the pointer upwards, and it will hit the menu bar and stop. (Fitts' law.)
Is it possible to have the best of both worlds: Separate spaces for my displays, but only one menu bar, located in my main display?
I just tested this on my new model Macbook Air with Lion. I see the same as you report: there is no "stickiness", the mouse cursor slides right past the Apple menu to the second screen.
I answered a similar question here - cmd-tab behavior on Mavericks with multiple displays
The Task Switcher does follow the Dock. If the Dock is on screen 1, the Task Switcher will appear on screen 1. If the Dock is on screen 3, the Task Switcher will appear on screen 3. Etc.
To make your Dock appear on a screen you can use a couple of methods.
Method 1 - Move your mouse to the bottom of the desired display. Don't stop once you reach the bottom of the display though, try to move it further down, as if you're pushing down on the bottom of the display with your cursor. This action tells the Dock to move to this display. This is temporary however, meaning the Dock will stay on this display until you perform this action on another display or reboot your Mac.
Method 2 - This will change the default starting point for your Dock. In System Preferences > Displays > Arrangement you can drag the menu bar from one display to another in this windows display icons. See the attached picture for reference. This alters the default preference to always show the Dock on the desired display, the one you drag the menu bar to in this preference pane, when you boot and/or login to your user account. You can still use method 1 to temporarily change the Dock's location but upon a reboot it will return to the display specified here.
Best Answer
There's no built in function afaik. However - even if you manage to hide the menu bar via terminal magic (don't know if there is) you will still face the issue that windows can't lap over the monitor (since windows can't lap between spaces), you can only move the complete window to one space/monitor or the other