It doesn't seem to broken. The capstone might be a bit of an encounter-ender, but that kind of what a capstone is supposed to feel like. The can't use again for 7 days part is weird. Custom made to blast Big Bads I guess.
The level 1 feature, Otherworldly Knowledge, I would change to proficiency in knowledge skills. If you are already proficient in the knowledge skill in question, then you gain expertise in said skill. I feel that is more balanced personally, especially when it comes to dipping.
The Level 14 ability I don't like. Seems absurdly powerful to me without a more potent drawback.
I would say you cannot use the capstone power against the same target for 7 days. It is only one minute of combat against a single target. You still have to hit them, if they escape your attack, you wasted the power. After one hit they may decide you are too powerful and flee.
Withdraw Memory is interesting, but it needs more clarification. It should be reciprocal, too, allowing you to share memories.
Forget balance, the mechanics are clunky and disjointed: Cha to Int skills, swapping out saves, a super powerful Detect Thoughts ability, and then an insanely powerful damage buff. It's all over the place.
I like the concept (warlock obsessed with knowledge) but I would change the concept so the patron is a god (of knowledge, secrets, etc like Thoth, Boccob, Oghma) using the warlock as a conduit to gain more knowledge. I would leverage some ideas from the Knowledge domain but be careful not to overlap.