How can I revert to showing cached pages when no database connection is available? [closed]

This is a response to your second question — “Also, it looks like the main page of the site is not cached, while everything else is. Is there any way to deal with that?”

In your backend, go to Settings -> WP Super Cache and select the Advanced tab. Look for the section titled Accepted Filenames & Rejected URIs. If Front Page (is_front_page) or Home (is_home) is checked, uncheck it, and then click the Save button. That should allow your site’s Front / Home page to be cached.

NB: This assumes you’re using the WP Super Cache plugin, which I gather from the question’s tags that you are.

(I haven’t tested this, though, so your mileage may vary.)