The PHP crash when you run it from command line, so it is not stable for production use. you need to find out which module cause the problem. Disable modules one by one see which fixes it.
You can ignore the first warning.
You need to fix /opt/lsws/fcgi-bin/lsphp5, it might be a permission problem if the file exist, try to run it from command line, and fix it according based on the error you get.
I am sure you will find answers to most of your questions if you read those tutorials.
1. Yes, you can use that.
2. same as vhost name, it should match the domain part of the URL
3. leave empty.
4. /home/rails/apps/appname
That's because the file "$SERVER_ROOT/404.html" does not exist.
You need to create the file first, you need to replace $SERVER_ROOT/ with the real server root, then create 404.html there, usually it is /opt/lsws or /usr/local/lsws.
If you need PHP, you need to build your own PHP binary, either through our web console or build it manually from command line.
http://www.litespeedtech.com/support/wiki/doku.php?id=litespeed_wiki:php:lsapi
make sure you have installed ruby-lsapi
gem install ruby-lsapi
check this tutorial
http://www.usefuljaja.com/2007/5/litespeed-ruby-on-rails-vhost-configuration
also
http://www.litespeedtech.com/support/wiki/doku.php?id=litespeed:wiki:template
You need to check the permission of statistics/ and logs/ directory.
Make sure 'apache' user can read access_log, does not get permission denied.
Try command
sudo -u apache more /var/www/vhosts/domain.com/statistics/logs/access_log