Did Eomer marry?
 

Did Eomer marry?

Yes. He married Lothíriel, daughter of Imrahil of Dol Amroth.

EDIT: crossposted...

Yes he married Lothiriel of Dol Amroth, daughter of Imrahil, their first child was Elfwine the Fair.

EDIT Yes I cross-posted too ha-ha

Please read HERE for the answer to your specific question.

And here is a link to the Encyclopedia of Arda where you may be able to find answers to many other of your questions.

You can also browse through 'Appendix A' at the back of The Return of the King book. Under the section "THE HOUSE OF EORL", subsection Third Line, are a couple of paragraphs on Éomer.

~*~ piosenniel