Changing the 13 inch screen resolution will unfortunately result in a less sharp display, simply because all these type of displays have an 'native' resolution which gives optimal results, leaving other settings less crisp. The 13 inch MBA panel has a native resolution of 1440x900, which is remarkable for a screen of that size (I have 17 inch widescreen monitors at work with that same resolution) but it can certainly be set at a lower figure.
The one area where the trackpad has benefits over a mouse is that you can use multi-touch gestures, just as on the iPad. That's a feature I really like, particularly being able to zoom in and out and scroll up and down, though of course other gestures are supported too. As such then it does indeed work much like the touch screen capaibilities of an iPad.
If you have a Mighty Mouse the one with the tiny scroll-ball on the top-front, then they are notorious for scrolling issues due to getting clogged up. They're not hard to clean, but the Mighty Mouse is notably inferior to the later Magic Mouse, which doesn't have a scroll-ball or wheel, but uses the whole top panel for scrolling using gestures in much the same way as a trackpad. I've found a Magic Mouse a good investment for any Bluetooth-capable Mac (which of course includes all MBA models).
[ON EDIT]: The MBA doesn't come with Flash, but it is a free download from Adobe, and is very simple to install. Just make sure you get the installer from Adobe.com and not any other location since there is some malware which masquerades as a Flash installer but is not safe to install! Beware though that Flash is very processor intensive, and if anything will run the MBA fans up to speed, and heat the system up, it is that.
Good luck with the readings!!