Discord is perhaps one of the most unexplored characters, past-wise. Like Scootaloo, we don't know his parents, we don't even know how he came "to be", he just appeared for the purpose of villiany. How did he withstand being stoned for 1000 years without going crazier than he is? What occupied his mind?

Why didn't he just take the Elements of Harmony?

Headcannon: Discord is more child-like than he even knows

The reason I think this may be the case is because the whole time of the Return of Harmony, he basically treated the situation like a game. He had fun messing around with the ponies, while causing chaos and getting what he wants. He's laughing even over a few silly jokes- and to let such a major deal slide under his radar is odd. As creatively manipulative as he is (and even kids can be clever), he treated the Elements like a tease for the Mane 6. Maybe he was so caught up in his fun, riddles, and jokes, that the act of fooling and causing havoc distracted him completely? It seems like he enjoyed the game more than the reward, and too careless to worry about it, it was his downfall.

It's also to be noted, after he won his "game", he fooled around with his little Chaosville instead of harshly demanding things from ponies. Chrysalis sucked the life out of Shining Honor and Cadence for her Changelings, Nightmare Moon wanted full tyranny over the ponies, Trixie demaned worship and special treatment.... Yet Discord did nothing but play with the ponies like little dolls, like a child would a new cat. Which leaves me to speculate that Discord treats ponies like toys for amusement and this was the reason Princess Celestia and Luna stoned him.

His "playing" may have gotten too careless, or perhaps Equestrian production became too slow and unproductive under his rule and constant play. Perhaps all his fun and games led him to cancel Pony school or stop production of silly things he saw unfit for Chaosville? And remember how arrogant(which leds to his downfall), and somewhat self-absorbed and indifferent to Ponyville's discomfort he was? Not to mention how Discord was laughing as he was stoned by the Princesses.

How did Discord know about the Elements of Harmony and the Mane 6?

Headcannon: Discord had a physicatic power, or perhaps he was told by Celestia

Disharmony and chaos is uncontrolled, pretty much, by anything but order and the Harmony. So, maybe Discord found a way in those 1000 years to travel in dreams, or learn some type of odd physic power(yeah, chessy, but possible in the show). After all, Nightmare Moon can travel in dreams, Chrysalis can physically transform into Princess Cadence. He has to have some loophole to let him travel in thoughts, or do something. Maybe he can't do this secret "power" if he's not stoned?

Perhaps Celestia told him, to intimidate him. But she wouldn't reveal the Mane 6's names and strong points, would she? I don't know, but Discord found out somehow. Maybe he can see into the future and forsaw the Elements. Maybe he's somehow connected to the Elements of Harmony after have been stoned by them and can "sense" the names, looks, and strengths (as well as Element) of each pony of the Mane 6. Just random theory here, I guess....

Headcannon: Celestia and Discord.... didn't happen

First off, Celestia flips out more so on him than any villian. Plus, if she truly ever did love him and feel any guilt as a regular lover did, why'd she leave him stoned for 1000 years(following my previous headcannon)? Not to mention how competely opposing they both are- Celestia hardly gets her hooves dirty and doesn't help the Mane 6, while Discord is a one-man show. He could animate several objects against the Mane 6 easily, but doesn't. He does it by himself, discords them by himself as the scene of the crime.

Secondly, Celestia is very collected, and I don't see her laughing at his silly jokes the way he does. She's possibly the least complex, to me, than the other characters- minor characters included(not background ponies). Discord is more complex than her, another opposite.

But, hey, maybe they could have had a fling? Highly doubtful though, I'll be interested if Dislestia becomes cannon in the show. I definitely don't see them coming together anytime soon, for obvious reasons: Discord locked away for 1000 years, then restoned in the Return of Harmony. Why would he be with Celestia?

Headcannnon: Like Discord, the Elements of Harmony can instantly appear anywhere in Equestria

Discord can magically appear anywhere. I don't believe the Mane 6 or Princess can call upon the magical elements when they so desire. But when used, the magic can be fixated on whomever it's focused upon, no matter how far away. Discord doesn't magically disappear upon his arrival in Ponyville in Keep Calm and Flutter On, because if he does, it'd be a moot point. The Mane 6 can focus the power on him while using the Elements and instantly stone him, no matter how far away, and Discord knows this. It probably wasn't revealed to the Mane 6 in the cannon, but I'm sure they would know this as well.

Headcannon: Discord had a jacked up childhood

Being given infinite power and being a draconequess probably had consequences. Maybe his parents abandoned him, maybe he was instantly shunned from pony society? Why isn't he so empathetic towards other ponies? Perhaps he was raised by wild wolves or abandoned and left to survive on his own in the wilderness as an outcast. And if he truly never had a friend, then this could be an explanation. Having the power he does, living in the wild would be easy because he could instantly make anything appear in thin air. Which, to me, seems a likely cause to why he treated ponies the way that he did if you follow my headcannon about Discord being more of a child than he knows. How did he see the world in his time of rule? Perhaps he saw it as an experimental ground to test his abilities, to test other ponies, etc.

Headcannon: Discord won't fall in love or will at least be blind to anypony's feelings

As much as I loved Keep Calm and Flutter On, I do not see him giving up easily to the forces of love. Assuming he never had a friend before in his life like he said, it took the loss of Fluttershy's friendship to see how much she really meant to him. I don't know how he'll treat future relationships, but I think he'll still be up in his old tricks... just not tricks that'll get him stoned. Like the Return of Harmony, I think he'll be too wrapped up in himself to really notice the love a mare feels for him (for the majority of Keep Calm Flutter On, he didn't notice the trust and benefit of the doubt Fluttershy bestrowed on him until she gave him her Element).

Plus, being alive as many years he has, and being stoned for 1000 years by the princess, I don't think any mare besides perhaps Fluttershy would be interested in him. Discord has too much bad mojo history about him, and, following my headcannon about him being very childlike, he probably wouldn't take it seriously. He didn't take Fluttershy's friendship seriously until he realized what he'd lose. How will he treat a full relationship? And, assuming he never had a friend until Fluttershy, we can guess that it won't be easy for him to be focused on the relationship. Discord may not spend enough time with the lucky mare, or he won't be able to "settle down" because of his antics and pranks. I don't think he's capable of having a relationship, but I may be wrong.