Can we make reporting objects that are in MRE as self service application?

Depends on what you mean by "Self Service". Can Reporting Objects exist without MRE? No. There might be a way to call the Report Assist from an HTML page or URL. The user would still have to be logged into MRE even if it's under the covers and they don't see it.

It would be a good idea to look into Quick Query. This allows for ad-hoc report creation in a self service environment.

Quick Query