By default key F10 is assigned to command Advanced - Run Windows Program in UltraEdit. This key assignment can be removed by opening Advanced - Configuration - Key Mapping, scroll in commands list to command AdvancedRunWindowsProgram, select this command, press button Remove and close configuration dialog with button OK.

A default system assignment exists as far as I know for Shift+F10 which opens the context menu like on pressing secondary (right) mouse button, or pressing the context menu key on keyboard if the keyboard has such a key. And by default key F10 without a modifier key toggles input focus between main menu of an application and previous input focus.

For example with key F10 not assigned to any UltraEdit command and caret is blinking in a file, key F10 sets input focus to File in main menu to navigate now in main menu using keyboard. And pressing key F10 once more moves input focus back to the file and caret is visible again. Or if the function list has currently input focus, F10 moves input focus to File in main menu and pressing once more F10 moves focus back to function list. But this standard behavior on pressing key F10 supported by all true Windows applications can be overwritten by applications as UltraEdit does by default.

Take a look on Keyboard Shortcuts for Microsoft Products and click on link to the page for the Windows version you use to get information about standard Windows hotkeys.

It should be no problem to use F10 for something different in other applications as long as F10 is for example not assigned to a shortcut file (*.lnk). Shortcut keys assigned to shortcut files are given a higher priority by Windows than shortcut keys in active application. Nothing must be changed in UltraEdit for assigning F10 in a different application to a command of this other application.

Please take also into consideration that other applications always running in background can define also some keys for some actions which have a higher priority than shortcut keys in active application. For example there are special keyboard enhancement applications preinstalled on some computers which execute actions on pressing some keys. Or with installing a display driver nowadays also additional background applications are installed and started automatically on Windows start. One of those applications always started with Windows start and running in background defines system wide hotkeys for example to rotate the display or toggle between different connected displays which can be disabled in advanced display settings configuration dialog.

It looks like on your computer such a background application started with Windows is running which performs the action to open last file in associated application on pressing key F10. Execute standard Windows application MSConfig, switch to tab Startup and look (on Windows 8/8.1 after clicking the link) which applications are started on your computer during Windows start. You can disable/enable those applications or you change the appropriate option in the application itself. Most applications have a checkbox option like Automatically start with Windows in their configuration/option dialogs somewhere which can be unchecked.