Make those paths writable. You need to change the permissions for those folders/files so that they are writable. You should be able to do it using your FTP client. If you don't know how to do that, ask your host and they should be able to help you.
1) Make sure your host is running cPanel. Many run their own custom panels that they try to play off as cPanel, but it's not.
2) Make sure you DO NOT transfer your domain name to your host. Keep it separate, i.e. on Namecheap or such.
3) Make your own daily backups that are off-site and...
The internal error is because your file/folder permissions are wrong for suPHP. It runs Apache as your user instead of as nobody. So the normal permissions won't work. If you change your permissions properly, suPHP will work.
DSO and FastCGI are both good handlers.
As I've said before, it's that most people don't care. Here on the forum, you get the xF enthusiasts and potential tinkerers, etc. But most people just install it, have their host install it, etc., and that's the end of it. It works, so there is absolutely no reason to upgrade. I can't...
Bandwidth is almost never the issue, nor is it very important, unless your forum is sharing a lot of files, images, etc.
RAM is usually the limitation when it comes to any website, not just forums. Disk I/O is very important as well, which is why most people these days go with SSD drives.
Can't help you there, unfortunately. I'm not sure what might be causing that, though all the sessions are stored in the database. If the database is having issues, I can only assume could do something funky with that list. But I don't know any specifics.