Each data type is typically produced from a single center. In most cases, you can find different types of data for a single patient, but each data type comes from somewhere else. Nevertheless, I think this is probably OK.

"gene regulatory network" is kind of a broad term. There are lots of ways to build gene regulatory networks, so I think you would have to describe a particular algorithm to get more detailed feedback. That said, I wouldn't consider it trivial to determine the run-dates within say RNA-Seq data (perhaps that information is somewhere in the metadata, but I have not personally found and used that information), so I think you should get downloading all available data for whatever you are trying to analyze.