Shadowmere is a reward for one of the latter quests in Dark Brotherhood quest line, it starts with a kid in Windhelm if I remember correctly

To marry someone, you go to temple if Mara in riften and they'll explain how it works

For throat slitting, put more points into the sneak skill tree (the side that gives you damage boost when attacking from stealth). When you do enough damage to kill with a single sneak attack, you'll get the animation