Yeah, honestly, the main reason I'm considering picking up the light novels is because I have no idea what's happening in the anime. And you're right, I have zero clues what Double Seven is and the next episode has a different title, so I guess whatever it was, I should consider it adapted and move on.
What I understood from these episodes were:
Double Seven is a pun on Saegusa's surname. Saegusa are the 7th of the Ten Clans. So basically the title is about the Saegusa twins because this 3 arcs have a lot of Saegusa's involment. The twins were meant to be the center of attention in this one, but alas they almost sidelined them.
The next title is easier to get because it is literally name dropped.
The fights were pretty neat and are super underwhelming in the adaptation. The anime desperately needs a narrator of some sort to explain what was going on during the fight for those that didn't read the light novel. It doesn't explain what spells they're using, why they're using them, or why it's impressive and/or why the Saegusa twins are so special (They have the exact same magical circuits, and can contribute equally to the same spells. Other collaborative spells have magicians do their own specific part, like how with the nuclear reactor episode before certain people did certain things in the experiment, like temperature control, gamma ray blocking, etc).
If you can get your hands on Volume 12 (double seven arc) and read chapters 14 and 16, you'll probably get a good idea if you want to swap over.
What's worse is that there's a lot of other things going on during the LN, and those so far have been skipped by the adaptation. More is going on with Shippou behind the scenes.
Even the fight between Tatsuya and Tomitsuka is horribly underexplained. A simple 20-30 scene with Shippou recognizing Tatsuya springboarding a counterattack of a same magic type block would have added so much depth. Literally the LN says that Shippou would have shouted "YOU CAN DO THAT" but was literally so shocked he didn't. That's why he was so frustrated at the end of the episode. He finally sees that he has room to improve and he's been arrogant and complacent thinking that he automatically deserves a spot in the Ten Master Clans, when those below him and beside him can easily beat him.
What's worse is they didn't even mention that the robot maid is literally an accomplice of Tatsuya's at the school, and was modifying spell cast data records in real-time. He tried using mist dispersion against Tomitsuka, which is one of his Trump Cards and literally national level security and privacy level magic.
It's really sad that they've given up on trying to give anything more than a surface level of the events in the anime because the spell system and politics are the best part of the series.
Even the first series by Madhouse had this poor understanding of the events, next seasons are just copying that model so I don't think they gave up because clearly they never tried. Also like many text heavy LN's, they expect people to watch the short specials that explain world and systems, but those series are never picked up by streaming services so...