problem with likes on email to subscribers and comments on posts

The Like button is indeed not displayed on Subscription emails, as we cannot currently handle Likes from emails for Jetpack sites. We’ll work on adding this to Jetpack, but in the meantime your readers will have to click and access your site to Like your posts.

You could force your readers to access your site to read your posts by splitting the content of your posts in 2:

• If you go to Settings > Reading in your dashboard, you can change your Feed Settings to “Summary”. Once you save your changes, all subscription emails will only include an excerpt of your post, with a link to continue reading on the site.
• If your Feed settings are set to “Full Post”, you can split the content of each one of your blog posts in 2 parts thanks to the More tag:
  <!--more-->

  Everything that is above the More tag will appear on your home page and in the subscription emails, followed by a link inviting users to click to continue reading; everything that is below that tag will only appear on the post’s page.

  You can read more about it here:
  https://en.support.wordpress.com/splitting-content/more-tag/

when comments are posted, they don’t seem to be appearing anywhere in the back end for moderation, they just disappear.

Do you use another Anti-spam, comment, or captcha plugin? If so, could you try to disable it and see if it helps?

Thanks for the likes info. Re comments: Yes we do, we use wpsecurity and a captcha as we were getting masses of spam coming through, will try that, thanks.

Seems to work when I deselect ‘Block spambots from posting comments’. Thank you!