This should probably be moved to the iLiad forum, or repeated there.
I don't have an iLiad, so I can't answer your specific questions about the keys. One thing to check is that the keys are being recognized. Do this in the keys tab under the options (crossed tools) icon, this tab is near the right end of the tabs and you may need to scroll the tab list to get to it. This tab allows you to bind actions to keys. You may want to bind the arrows to large scroll forward/backward. I have an example of this on the PepperPad 3 in
Visual Tour of FBReader.
The arrow icons are not next/previous page but rather go forward/back (redo/undo) a major navigation operation. If this sounds hazy, its because I'm not actually sure sometimes why one operation invokes the arrows and others don't.
Another thing to check is that a "standard" e-book works as expected. FBReader does well on DRM-free MOBI files (which you can also check using MobiPocket Reader). There are lots of these for download from MobileRead, but they don't have a formal TOC and are therefore less like CHM files. A book I have used as a test is
Ring of Fire from the Baen Free Library. Download the Palm/MobiPocket version and see if it works with FBReader on the iLiad. You should get an active TOC icon and the page bar should have section line markers.