Hello,
As we click on "All issues" on projects page
(New project | View all issues | Overall spent time | Overall activity )

URL seen is : http://myURL/redmine/issues

I save a query with filters as
(Issue is Open and Project = All my projects)
with name as "Open Issues from all my projects"

The URL is seen as
http://myURL/redmine/issues?query_Id= 1;

I see an issue list from all my projects (Pr1, Pr2 etc)

But as I open one of the issue from Pr1, the query turns specific to Pr1, clicking on the Custom query, shows open issues from Pr1 only.

This happens because, ?query_Id = "some_id" is appended to the URL.

The URL is now
http://myURL/redmine/pr1/issues?query_Id= 1;
and not the one I created as
http://myURL/redmine/issues?query_Id= 1;

This goes against my thinking when I created the query, as I am not viewing Issues from All My Projects now.
Is there any way to avoid the confusion ?

I would suggest: create a separator : All Project Queries bellow : (Public) Custom Queries.