What do you mean 'Group Wall' widget?

By default, Groups don't have widgets on its profiles but the groups' modules only.

Do you use a 3rd party plugin?

The widgets are from ColdTrick's 'Widget Manager' and 'Group Tools' plugins. Forgot about it.

Just tested with the followed steps and all works very well:

1 - Add in start.php of your custom plugin:

elgg_register_widget_type('wall', elgg_echo('wall'), elgg_echo('wall:widget:description'), ['groups', 'profile'], false);

2 - Add 'Wall' widget on Group's profile

3 - Check on 'Show a form to add new posts' option in the widget's settings

4 - Done.

Tested on Elgg 2.3.14 / hypeWall 5.2.0 / Group Tools 9.4 / Widget Manager 8.3.2-1

1 - Don't use elgg-data in the name of Elgg data directory.

Use data instead. (As suggestion, don't use any symbols/characters excepts letters and numbers.)

2 - Check your settings file:

/var/www/elgg/elgg-config/settings.php

Look at these params:

$CONFIG->dataroot

$CONFIG->wwwroot

3 - Try to disable system/simple caches settings on Site settings page in Administration.

Clean the caches and check you site again.

4 - Enable the logs on Site settings page in Administration:

Note: cache folder doesn't exist in data directory, caches only. The links as you mentioned are correct and not related with folders in /data directory.

More info on http://learn.elgg.org/en/stable/admin/index.html