Regarding the comments counter, it will only work properly when the article "title alias" is not changed and the "state" of SEF or no SEF URLs in Joomla! is fixed (e.g. SEF is on or off).

If you change any of these 2, e.g. manually change the "title alias" of an article or if you contantly switch on or off SEF or change SEF components altering the whole time the resulting URLs of your articles, then the comments counter will break.

It will break because it uses the page's actual URL each time to fetch the count.

So, just make up your mind with URL, don't change the title alias on articles and your comments counter will always work. Otherwise, just choose to hide this element in the plugin parameters. ;)