The flipbar, up-arrow, enter, down-arrow and "up" (staircase) keys are all potentially recognized by FBReader, as are the "long" versions of all these keys. Only a few of these are bound to "actions" by default. To remap these keys, select the options panel icon (tool or crossed tools) and then navigate to the "keys" tab (which may initially be off the right edge of the options window - get to it using the small right arrow near the tab labels or using the right arrow key on the on-screen keyboard). Then bind each key to an action selected from the pull down menu.
Full screen mode is broken. As you say, you can enter it but can't get out again.
If you have characters that don't display as expected there are two possible causes: (a) the encoding is wrong (select from the info menu for each e-book) or (b) the font does not support the character. For (a) the usual "Western" options are ISO-8859-1 or windows-1252. For (b) try using DejaVu Sans, which typically has support for more unicode characters than other fonts. Fonts are selected under the format tab of the options icon.
There is a wiki entry for
ILiad FBReader.