Disclaimer: I don't own Naruto.
1. Anko was not the only one to survive the curse seal, just the luckiest. Iruka will never become a jounin and Hayate is dying slowly.
2. True kenjutsu masters are incredibly rare. Orochimaru preferred to use his other skills, but he recognised talent when he saw it. Gekkou Hayate was taken out of the Academy the next day.
3. Unlike most teams, the rivalry was not between the boys. Anko didn't understand Iruka's grief over his parents (hers had died before she was old enough to really remember them) so she dealt with it the only way she knew how. Two weeks after the attack, sick of his moping, she woke him up with a bucket of water. He retaliated with neon green hair dye. This started a prank war that only ended when their sensei found that Kusanagi had been replaced with a rubber chicken.
4. It was Hayate that gave him his scar though. Orochimaru's training methods were questionable at the best of times. However, practising taijutsu next to someone going through katas with a sword nearly resulted in Iruka losing an eye when Anko ducked and he didn't realise why.
5. Orochimaru did not show emotion when he learnt of Hayate's death. Kabuto was punished for allowing himself to be spied on. On the other hand, Anko and Iruka went on a bar crawl and dragged Yuugao along. They collapsed on the floor of Iruka's apartment and woke up with no idea how they'd gotten there. This ended up being a yearly ritual. Everyone else is smart not enough to comment.
6. Once Iruka teased Anko about being a year older than them and implied that this meant she had been held back. She proceeded to demonstrate her mastery of the Snake Hands jutsu to prove him wrong.
7. All three are capable of summoning snakes, however none do it regularly. It drains Iruka's chakra too much to produce anything useful in a fight. Anko avoids it as it reminds her of their sensei. Hayate worked on mastering kenjutsu instead.
8. Most people think that Anko broke the unwritten rule that kunoichi fall in love with their teammates. This is true to a certain extent. She has never loved them but she would die for them and that's all that matters to her.
9. On the other hand, they do love her. To Iruka, she is the big sister he never had (and wishes he still didn't sometimes). Hayate already has several older sisters. He treats her like his younger sister despite the fact that she is the elder. Both boys have jumped in the way countless times because she never thinks about the danger and can practically guarantee that they will have to keep doing it. (It's worth it to keep her safe.)
10. Iruka is the one who confuses their sensei the most. He sees himself in Hayate and Jiraiya in Anko although if Jiraiya comes anywhere near Anko, he will use Kusanagi to castrate him. There will be no perverts on this team. Then he sees Iruka patching up Anko after she got into a fight and realises that he is the Tsunade of the team. There is almost nothing in common between Iruka and his sensei. Coincidentally, he also is the one who uses Orochimaru's lessons the least.
11. When they get out of the hospital to discover that Orochimaru left and took Anko with him, Hayate and Iruka have to be watched to make sure that they don't follow them. This is more difficult than it seems. Iruka is an ex-master prankster and Hayate is remarkably capable of fading into the background. Eventually after they've given half a dozen ANBU the slip, Kakashi and Itachi are assigned to keep an eye on them.
12. Six months later, Anko returns and only then do they learn what the marks on their shoulders mean. By unspoken agreement, they cut Orochimaru out of their team photos and never call him sensei again in public.
13. Every year until Hayate's death, the three of them visit the memorial to remember the people who didn't survive the seal. After the invasion, they go to it on the day he died instead. When Sasuke leaves for Sound, they think perhaps they should have brought him, and explained the price of power and the true nature of Orochimaru.
This was inspired by sketches of them on Deviantart. Also I'm a big fan of Anko and Iruka, especially anything involving both of them. The first and seventh ones implied that the seal messed up Iruka's chakra. Orochimaru doesn't seem to use Kusanagi much but it was obviously important enough that he taught Sasuke to do it, so he might have taught someone else as well. Finally, this is as canon as I can make it which is why Anko is a year older than the others. I did fudge a little on when exactly Orochimaru left but I don't think Kishimoto ever tells us precisely when that happens.