“I’ve tested it under normal Joomla and it works but WT Atique isn’t”
Do you mean with SAME TEMPLATE CONFIG with default Joomla template and it works ?
Submit the private ticket here https://warptheme.com/member-area/ticket-system/ with username/pwd to check.
“2. Is it possible that some page sections do not appear after login?”
Quix does not support the access level per SECTIONS. I mean the Quix built-in elements.
However, if you use Joomla module inside Quix page builder, you can use Joomla access level for the module you wish to hide for guest/registered.