We have a Count field for many things that are exposed for reporting only.  So for Views to simulate a count you would need to create a custom Integer field with a default value of 1 that is never changed.   Expose that field in views and roll up your sums with it checked.  We did this internally and I believe it works quite well.

re: issues.  Yes, the Issues Tab view will show all issues in the system from any project type/project that the user has access to - it is native to our system and can be a definable view(s).

I think you are asking if there is a "public" view that shows everyone all issues from all project types?  If so, then no - it would have to be a report -unless every use in your system was a member to every project.

 Ahh - unfortunately the executive tab only exposes Project fields (and a handful of other odd fields).  The goal there was to allow the drill through of a project to get to specific issues/milestones and other basic data, not to display item details all on the scorecard view.

You have a good idea - of combining Issue fields (or all app fields) however that would be pretty tricky to design and display if you mean integrate a project's issues right onto the Executive tab view.  Something like this:

But maybe more issue detail or something? The trick here is that the Exec tab lists projects as line items so how would you display a lot of issue information inside a single project line item?  It could be done as a simple list of issues probably as seen in the mockup above.

The best you could do is invite all execs into every project as a guest (could be a modified guest role depending on control) and then expose the Issues tab with some pre-defined views that shows the issues in a smart way.  

Exec logs in and hits the exec tab for project info, and issue tab for issue info.   

if you have a WI license you could create and push a dashboard view to your execs with a report that gives them project and issue info in a summary style report.