I don't have the equipment at hand to test this, so before melting my brain on this, this is the scenario.
Suppose that you are playing a FPS with your mouse set at 1000 DPI and your in-game sensitivity at 5. How would your game experience change keeping the same DPI but changing one or both of the other two variables, screen resolution or screen size?
Same DPI but lower/higher resolution: would you have to readjust the in-game sensitivity to keep feeling the same? If the sensitivity remains the same but you have less/more pixels to travel across, will you feel your mouse more/less sensitive?
Same DPI, same resolution but different screen size: if you keep everything the same, but the screen is bigger/smaller, will your mouse feel more/less sensitive because by doing the same wrist movement your cursor will cover more/less screen space?
Best Answer
As far as my understanding goes, screen size is not important. It's rather the screen resolution that is important.
In the simplest (non-existent) case, each dot on the mouse's pad corresponds to one pixel on the screen. So, for example, if your screen resolution was 1920x1200 and your mouse was capable of a maximum DPI of 600, you'd have to move your mouse two inches to get from the bottom of the screen to the top. If your mouse used a DPI of 1200, it would only take one inch to make the same movement on the screen.
Therefore higher mouse DPI allows you to move faster on the screen with less mouse movement. Higher resolution displays may require higher sensitivity or higher mouse DPI to attain the same amount of on-screen movement, or one would need a ridiculously large mouse-pad.
Sensitivity is software based. It gets your dpi and divides or multiplies it to get the final dots-to-pixels sensitivity. It is just a multiplier of the input sent by the mouse. For example, if you had the mouse on 3600 DPI and then set the sensitivity to 2.5/10, it would function the same as 900 DPI on 10/10 sensitivity.
There are cases where mouse sensitivity in the supplied mouse driver is applied in addition to Windows mouse sensitivity, it all ending with an unpredictable mess.
So, for your questions:
Same DPI but lower resolution : Mouse will cover larger physical screen territory with the same hand-movement. It will be harder to click exactly on a specific small area on the screen.
Same DPI but higher resolution : Mouse will cover smaller physical screen territory with the same hand-movement. Working with small screen objects is easier as the mouse is "slower".
Same DPI, same resolution but different screen size : Getting from one side of the display to the other will take more mouse movement. But if the same windows are displayed in the same size, working inside such a window will be the same. For getting faster across a large screen, you could use mouse acceleration together with fast and large gestures. However, in gaming mouse acceleration can make you overshoot your target.
Both higher and lesser mouse DPI have their advantages. I am, for example, currently using a mouse that has a DPI switch button, so I can change the DPI to suite my current task.