This plugin finds YouTube links in post content and imports the video comments.
Posted comments are often delayed by a short time, even though they appear immediantly on YouTube.
Sign out only cancels the ability to post comments. Users can only sign out completely from YouTube/Google.
A developer account is only required to post comments. You can show comments without a developer account.
The redirect URI must exactly match your site's URL. An extra trailing slash is enough to cause that error.
Yes, a setting is provided for custom fields. YouTube Comments supports the "Automatic YouTube Video Posts" plugin, and the "deTube" premium theme.