WordPress comments work locally only?

Here’s my issue:

• on localhost: comments just work for both registered & logged in users AND for guests,

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  • Comments on Author page
  • Why are authors allowed to approve comments on their posts? How to revoke privilege?
  • Success message in comment form

• live (on-line): comments work only for registered & logged in users, comments posted by guests are “disappearing” on the way, they’re not being shown under “Comments” in wp-admin, and after posting them browser scrolls all the way top instead focusing on newly added comment to approve.

Of course I have “Users must be registered and logged in to comment” unchecked. Is it possible there’s some issue with my server configuration? I’m using a custom theme, but the comment system is exactly the same as in other themes from twenty* line.