These are widgets and not modules. If you want to customize the output, feel free to edit the theme files,

Events:
/media/com_easysocial/apps/user/events/themes/default/widgets/profile/events.php

Groups:
/media/com_easysocial/apps/user/groups/themes/default/widgets/profile/groups.php

I was not able to do it. Still displays only user-created events. In version Easysocial 1.4.10 display events to which the user attending

Hi Albert,
By default, the creator of events will automatically attend events. So even if created events is not shown, those events will still show under attending events because the creator is attending them. Perhaps you can try to set the creator to 'Not attending' for those created events and see if the event will still show up on the attending list(http://take.ms/vIExB).
For groups, it will always show the groups the user is involved in(created/joined). This behavior is determined from the getGroups function in (JoomlaFolder/administrator/components/com_easysocial/models/groups.php) and (JoomlaFolder/media/com_easysocial/apps/user/groups/widgets/profile/view.html.php).

You misunderstood me. I just want to have the widget display a list of events in which the user participates. Now there is displayed the list of user-created events

Hey Albert,
By default the widget will display both attending and created events of the user in that profile page. In other words, you should be seeing the attended and created events of the profile that you are viewing. If you are not seeing the events that the user is attending, then we need to investigate this on your site.

Yes in the file it is written but in practice are not shown events in which the user will participate. On your demosite sign Darius Scott b view. In previous versions, everything displayed properly

Hey Albert,
My apologies. It seems I did not have the right conditions to test this. When I view a user profile that has attending events only(no created events), the events widget did not show.
This is because the logic is incorrect in this file: JoomlaFolder\media\com_easysocial\apps\user\events\widgets\profile\view.html.php(http://take.ms/huolJ)
It should show the widget when the user has EITHER created OR attending events. This fix will be included in the next release.

Also, do note that expired events will not be counted in the user profile header or events widget, thus the number '0' that you see in the demo site.

Yes. Now everything is fine.

Hey Albert,
Understood. Glad to hear that your issue has been resolved now.