Yes, he was married to Lothiriel, daughter of Prince Imrahil of Dol Amroth, while he stayed in Gondor two or three years after the book ended. He later died in the year 63 of the Fourth Age of Tolkien's Calendar, after having a son, Elfwine the Fair.
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27/28. (It's impossible to tell as the date of Eomer's birthday is unknown.)
Your question is a little unclear... but maybe fanfiction . com? That's the only place I can think of.
Hasufel was a horse of the Rohirrim, ridden by Garulf of Rohan. After Garulf's death, Hasufel was loaned to Aragorn by Eomer in recompense for the accidental and only apparent slaying of Merry and Pippin by Eomer's riders. Aragorn rode Hasufel to find the hobbits taken by the orcs, and to Helm's Deep. There, Hasufel was returned to Eomer. From there, he was probably ridden to the battle in defense of Minas Tirith with the forces of Theoden.
No, Éomer does not die during the narrative of The Lord of the Rings. In the Appendices we are told he lived a (for his people) long life, dying in his nineties.
Harry and Ginny get married, Ron and Hermione get married, Molly and Arthur weasley are married, Lupin and Tonks get married, Lily and JAmes potter were married. Fleur and Bill get married. George weasley and Angelina Johnson get married.