I don't see topics which are on widget screenshots.

Another point is the permissions, maybe Guests doesn't have permissions to see missing topics. Make sure Admin and Guest View permissions are the same for these topic forums.

Here one of them named Testing Parts!!! that is shown in Recent Topics widget.

The others are Recent Topics which does not show in that widget.

And issue which does not show all Recent Topics is related to permissions,you were right.

Recent Topics widget shows recent topics by created date, not by modified/updated date. You can see the topics' recent activity in Recent Posts Widgets. The idea of Recent Topics widget is displaying the last topics, not last replied topics. It seems all is correct on your end.

On my site they display not Recent Topics but some old topics which i had to edit recently due to code left by GD BBPress Tools plugin.

Just for testing i have edit one old topic it shows now in Recent Posts widget as recent post.

Is this normal or it happen only on my site?

Could you please insert new normal topics, say 2-3 new topics, I need to see if all works fine with new topics.