Your formula is correct.
Your display has 86 pixel per inch, which is very low. Your pixels are larger than that of the vast majority of displays.
An equivalent resolution 17" display (which existed back when these displays were new, and probably still exists) would have 96 pixel per inch; you get the same with 15.4" and 1280x800, 20" and 1680x1050 and 23" and 1920x1080.
The current trend is to go slightly above 100 pixels per inch (2560x1440 at 27", 2560x1600 at 30", 1440x900 at 15").
While a display with your pixel size might exist, I'm afraid technical advances have reduced or eliminated your chances to find a matching display. Correction: There are 27" displays with 1920x1080 or 1920x1200 at 82 and 84 pixels per inch respectively. This is probably your best match. There are also a few TV displays in that size and resolution.
What you call “internal resolution” is the native resolution; that is, the resolution that maps correctly to the LCD screen (1 pixel of resolution to 1 physical pixel on the screen). Any distortion, smearing, etc. is caused by the display trying to map a non-native resolution to something it can display. CRTs don’t have native resolutions and are generally able to scale any resolution up to their maximum without problem.
When you connect an external monitor, if it is an LCD or projector, it too will have a native resolution and may be different from that of the built-in display. If it is a CRT, then it won’t have a native resolution, and it should be able to display anything up to its maximum.
Also, when you connect an external display to a laptop, you get multiple displays in the Display Properties dialog (assuming Windows™) and should be able to set the resolution for it independently from the internal display. So when you do connect one, just set it to whatever resolution you want if it’s a CRT or if it’s an LCD, to the native resolution of that display (not the internal one).
That said, if you want to use a really high resolution, you will need to make sure that your laptop’s graphics chip can support it, though most video adapters from the past decade or so can support at least up to 1600, even in laptops. Pretty much any projector under $1,000 will be limited to either 800x600 or 1024x768, so that won’t be an issue because your laptop will almost positively be able to do that. However if you intend to connect a monitor, you’ll want to confirm that your display adapter can support the resolution you will use (the res you want for CRT or need for an LCD).
It should be easy enough to find out what resolutions your display adapter supports by checking the Display Adapters branch of the Device Manager to identify your graphics chipset then Googling for its name + maximum resolution.
Best Answer
That is correct. A smaller monitor with the same resolution has a higher dot pitch.
Not necessarily. It depends on what you want the larger monitor for. If it's for vision problems then an equal or lower resolution may be preferred.