I'm having security access issues and am wondering if there's a bug
or quirk with SharePoint I'm not aware of. I created a subsite using
unique permissions.

Tired of people looking at the People and Groups area and asking why
they were in one group and not another, I created a new site
permission on the site collection level. Site Permission: Contribute
minus Browse User Information.

The issue is: My users can add and modify, but can not delete
anything--whether in document libraries or lists. There is no
explanation from the SharePoint front-end side of things, and while I
have SharePoint Designer, I am new to it. One user, who was even
listed as site owner, had access issues in adding to the contact
list. They keep getting the error screen, you don't have access,
please login as someone else--when their permissions are inherited
and they clearly have been given read/write/delete access.

Is there a Microsoft bug regarding modifying site permissions? In
SharePoint Designer, how do I see security from a site level (not
just by list or library--which are grayed out since they are
inheriting permissions). I'm hoping there's some invisible security
box checked somewhere in Designer that I can uncheck or such.