Welcome to problem solving.
But seriously, look at the errors that application is throwing up, especially those errors like the one where it can't find things like that /statuses/update.xml file.
You can't hold the webserver (in this case Litespeed) responsible for things like the structure of the filesystem you installed the application on top of. If the application is looking for a file that isn't there, or isn't in the right place, it is unlikely to be Litespeed's (or Apache's or nginx's etc) fault, but is much more likely to be an installation error.
And if you can't figure it out, hire a friendly PHP coder to help you out. The $50 or whatever it may cost you for 15 minutes of their time looks like it might save you hours of problem solving time, so it will be worth it.