The is no problem with Theme Options saving on my localhost test site.
You will have to troubleshoot to find out what’s causing this issue on your website.
First of all you can do troubleshooting by disabling one plugin at a time, to find if any plugin is causing this issue.
You can also disable all plugins and see if your theme options will save.
Please get your web hosting to look at your server error log for anything that says fatal error. Post here if you see any. Ignore warnings…etc. Warnings do not cause issues..
As for the number of footer columns, there is only 4.
If you need to increase, you will have to hire a developer for this modification.