Thanks for you answers.

At this point, as single site admin I can see URE under Users and under Settings, but not under Plugins.

URE is available at single site “Plugins” list (multisite) under the same condition as it’s available under “Users” and “Settings”. User should have URE’s key capability. It is ‘manage_network_plugins’ in case URE_ENABLE_SIMPLE_ADMIN_FOR_MULTISITE constant is not set or ‘administrator’ – the same as for single site, in other case.
So I understand when you report the 1st issue, that single site admin does not see URE at all. But I don’t see the reason for the current state. Add here the fact that I can not repeat this issue at my test WP multisite, where single admin sees URE under “Plugins” of his site.

Is it possible to get FTP and superadmin access to your test WP mulitisite installation in order to try to find the reason of the problem?