1. Latest version of a Web browser
Tested with Chrome/Chromium and Firefox on Linux, and same plus Safari on Mac. It may or may not work on Internet Explorer (theoretically it should, with versions 10 and above) -- I don't have it, and would not develop for it, or fix any related problems.
Although it is a browser-based application, a Web server is not required -- you can run it by pointing your browser to a local file on your computer.
2. Screen resolution above 1000x600
3. The interface has been designed for real computers with a mouse or a touchpad. I have tried it on an Android tab -- it does work, but the interface is not particularly easy to use. As for iPads -- I have no idea.