You're not getting to the limit of your Android abilities, you're expanding them!
To add the application to your launcher is normally fairly easy, it depends which launcher you have on your device. If you can see an Add button somewhere on the launcher's homescreen, click it, locate Live Sports and tick it.
If you can't see an Add button, bring up the list of all installed Android applications (from your launcher, not XBMC), locate Live Sports, and try long-clicking on the icon. With some launchers (including the default Android one), this will allow you to create a new shortcut on your homescreen.
To add a shortcut to the app within XBMC itself, head to the System menu in XBMC. From there, you want Appearance, then Skin Settings.
The exact name of the next menu you need will differ, depending on which skin you're actually using.
http://goo.gl/Y91Sz2 links to _andapk_fifalivetv_v2.apk
and
http://goo.gl/JfAzvf links to _andapk_pub_lst_v2.apk . I couldn't find much useful on the first file, and for the pub lst file, there was an Arabic language forum where someone suggested using, translated version here -
http://translate.google.co.uk/trans...7/archive/index.php/t-565574.html&prev=search
If you get too lost trying to locate downloaded files, you could search for them with ES File Explorer, as long as you know part of the filename. Click the search icon at the bottom (with a magnifying glass) and type in the name of what you are looking for - though I'd be surprised if it wasn't in the download folder!
I think it was Live Sport that recently had an update that didn't work on some devices - if this proves to be the case on your model, head to Android's Settings>Apps>Live Sports/Live Sports Pro and check if you can uninstall the update. If not, uninstall entirely, and use the original APK to reinstall the earlier version. (If you can't see an Apps submenu when you open settings, click on the last tab and select the More/Advanced Settings button).
Re the picture size, is that JUST in Live Sports, in XBMC or with ALL Android apps, and the launcher itself?
If all apps have been effected, head to Android's Settings and look for a Display/Screen submenu, there should be options there related to changing the screen scaling and resolution. Check which settings look best on your screen, and if it goes completely blank at any point, don't click anything for 20 or so seconds, and the device should automatically revert to your previous settings.