Can I force a higher resolution on my PC and monitor?

No. If it were a CRT monitor, you MIGHT be able to ever slightly at the sacrifice of refresh rate (vertical scan rate), but pushing the hardware to its limits can cause failure.

LCD monitors have one fixed resolution at which everything must be displayed.

I just bought a cheap 2nd hand LCD monitor with a native 1440x900 resolution (thing is 19'). I've set a manual resolution of 1920x1080 and it's working perfectly. Though the lettering might be small, it does show the screen normally. Have to add that the native resolution can be set to 75Hz, and I've set 1920x1080 on 60Hz.

You can't increase your screen resolution past the capabilities of your graphics card and monitor.

If your using the maximum resolution - thats as far as you can go.

Ofcourse, you can upgrade your graphics card which will entail in better graphical output and in toe, better screen resolution.

I noticed your using 1920x1080. This is a high-definition screen resolution, many high definition TVs run on 1920x1080, you really can't get any better, well you can but the difference is the size of the screen in dimensions only get bigger, not technically better, but your already at that milestone of high quality graphics, you shouldn't need to go further!

No. The resolution is a hardware limitation. And why would you even want to?