The behaviour you are seeing with the links is as intended.  When you see a particular requirement inside a module, that is actually a requirement being reused in that module.  The requirement also exists as a stand-alone artifact in the folder hierarchy (you've probably noticed the folders that live beside modules and which are created with the same name as the module - they contain the stand-alone artifacts).  We refer to these stand alone artifacts as "core artifacts".
When you create a link to a requirement, you can either link to "the requirement in the module" or to the "core artifact".  If you link to it in the module, then the link you create is only visible when you look at the artifact from within that module.  If you create the link to the core artifact, then the link is (optionally!) visible in every module where that core artifact is reused.
The bit that surprises me here is that I would have expected the dashboards to still work (for instance, the recent changes dashboard widget shows modifications to both core artifacts and artifacts in modules).  Similarly, I would expect reporting capabilities to see these links (but only attached to the artifact in the module, not the core artifact).  However, I'm not an expert on the reporting capability so perhaps I am wrong on that front.

I hope this helps.
-Dominic

Hi Sany,
I see what you mean, there is a gap here.
I've created enhancement 77198 (Working and linking within modules is not compatible with dashboard widgets like the "Requirements View" (77198)) to capture it.
For the traceability views, are you referring to the "configure links to show as a tree view" option in the artifact grid display and the fact that it is absent in the module display?  For that issue, we do have traceability columns in the module grid which can provide a slightly different experience (I guess you've seen those and they don't do what you need?).  We are also investigating a stronger traceability capability currently which should play nicely with links from within modules (but I don't have details or timescales at this point).

In a module, you can add traceability columns, each of which shows trace information for one particular link type.  These columns can also show up to three attribute values from the other end of the link (this mechanism works within RM data but you cannot see attributes if the links are to another domain such as RQM).
You can add a column showing "Validated By", which will show the test cases associated with each requirement in a module (and then rich hover is available to see more details of the test case).  Unfortunately, you cannot show attributes from the test case directly in the column.  One thing you can do, however, is filter on "lifecycle status".  For instance, you can filter your module to show only the rows which have a failing test case linked to them (see "Filter by Attribute/Limit by lifecycle status").  These are the mechanisms I was referring to, which are not a replacement for the traceability capability in the grid, but which might prove useful.

The "traceability" capability in the artifact grid is limited to links to the core artifact as you have already seen so the only solution there is to make the ValidateBy links from the core artifacts instead of within the module (if you make the links from the RQM side then this is possible by finding the artifacts directly in the folder hierarchy instead of within the module.  If you are making the links from the RM side then it's a bit trickier, but you can do the same thing by finding the artifacts in the folder hierarchy and making the links from them).  I recognise that this is not ideal and I've added a note to 77198 including this case.
I hope this helps.
-Dominic