I have seen that this forum does not consider it inappropriate when some member makes a post or thread about a competing forum. I am a member of other popular forums and they do not allow mention of competing forums as it is free advertising for them.
I doubt there are many forum or similar places which do such thing.
What is the opinion of members about this?
It's poor suggestion.
Is it fine allowing members here to promote or mention competing forums without paying this forum owner or taking his permission ?
Yes, we already can discuss service on "Service Discussion" and promote service on "Service Announcements". Even social media doesn't forbid you to talk about competing social media.