Can a rejected manuscript be submitted to another Elsevier journal?

In general, when a paper is rejected, you can resubmit it to another journal as soon as you feel you are ready. There is no minimum waiting time, and it doesn't matter whether both journals have the same publisher or not.

As far as I know, publishers don't generally share information about submissions between journals. (However, it could happen that the second journal would require you to tell them about any previous places the paper has been submitted.)

In theory some publishers might have special rules, but I've never heard of this.

[EDIT: I just submitted a review, and there was a little box ticked, saying]

In the event that this manuscript is rejected by this journal and transferred to another E******* journal I agree that this reviewer report, my name and email address may be transferred alongside it.

[This corresponds to the second point below]

So, unless you are banned by a society and forbidden to publish in their journals for some reason (e.g. plagiarism), there are fences between two different journal submission systems. And no rule known to me.

However, two aspects require caution:

• close journals, especially with the same publisher, may have the same editors, area editors, etc. It is interesting to check the editor list and check for an overlap
• since reviewers are hard to find, I suspect that a publisher may have a database of all its parts reviewers (whatever the journal). So with a similar paper, the same keywords, you might as well end up with the same reviewer. Who might have mixed feelings about reviewing "the same paper" twice.

From what I understand from your question, your paper might have been mildly reviewed, possibility checked by an editor, who made the decision himself. So the second point might be as less concern.

It depends upon the reason for the rejection.

If your science is fundamentally flawed and the paper in written particularly poorly, then I imagine that resubmission is not advised (to any journal).

Alternatively, if the paper is high quality but is rejected for addressing the practical aspects of a topic (whereas the journal in question deals only with theoretical aspects) then it may be perfectly reasonable to resubmit to a more appropriate location without modification.

I cannot answer your further questions about data sharing, though I believe the other answers begin to address this.