Grammatik und Zeichensetzung
Let me begin by saying that I read all 16 chapters in one sitting. I haven't done that in a while but your story didn't let me even go until there was no more and my heart was crying in the corner.
Lies die Geschichte jetzt
I found it very fresh and unique - not the whole supernatural-wanting-to-claim-his-unwilling-mate-who-later-falls-hard-for-him but your take on the concept. Elyse is super intriguing and interesting even though I thought she was too timid in the beginning. I do understand her slight inferiority complex but she is a fighter and it is so beautiful to see her waking up to realize that.
And of course, I am a big sucker for strong, terrifying males with possessive instincts(don't judge) so you got me there. I think it was really smart that you chose a demon(vampires and werewolves are really overdone) and that you kept his almost-human but not quite. The nails part was just the right magical ingredient that made it come to life for me.
There are some things you can work on though and you should if you plan to publish it one day.
You tend to put your characters in a blank space where something happens(or not) and they just talk. This was happening mainly in the first chapters but I've noticed it later on as well. The conversation goes well(or the action scene) but the reader is disoriented what, where and why is happening. One example is that summoning and then the following chapter. This is your beginning, your chance to catch the reader in your snare - make it an inescapable one. I know too much description can terrible and people will skip it but same applies for two little. Focus on the important things - what Elyse feels under her feet, her hands, her cheek(she was lying on the ground). How does the room feel, why? If she whimpers make the reader whimper, if she takes a sharp breath the reader should too. If you manage that you;re all set - they will forgive you everything :D
Anyway, there are some stylistic things you can work on but this seems like a first draft so I'm sure you'll make it all nice and clean once you get to editing it.
Good luck and post the next chapter sooner before I go and summon a demon on my own.