- Touching antennae as a friendly greeting (brief touches in more casual/formal settings, longer and more information-rich touches among friends and loved ones)
- Queens as revered philosophers/poets/mathematicians/etc. (critical to a hive’s survival so kept healthy and comfortable, lots of time spent sitting around pooping out eggs and probably wanting something stimulating to do, bodies not really suited for most physical activity)
- Cities are half-buried arcologies that are dark and claustrophobic by human standards but resulted in strong institutional knowledge of engineering closed systems which means (if in an interstellar sci-fi setting) they contribute a lot to the galaxy’s orbital habitat/spaceship design
- Children raised in communal creches by a class of dedicated workers, they don’t really have a “parental instinct” as we understand it but their childcare workers are the best you could ask for. They view the nuclear family as akin to a society where everyone has to build their own car in their garage instead of just taking a damn train
- Their equivalent to the neolithic revolution was the rise of poly-queen societies, that is, polities that could organize around and maintain internal cohesion with multiple queens


In addition to Children of Time, another book with Giant Intelligent Friendly Talking Spiders is Vernor Vinge’s A Deepness in the Sky. Culturally they’re, hm, sortof similar to a kind of 1920’s pastiche - but a big part of the story is about translation and observation. The Spiders (in CoT and ADitS) have very different sensoriums, with much more focus on reading surface vibration over being able to hear, it might be interesting to decide how the hive creatures sense alter their recording methods.
Vinge’s other book in the series, A Fire Upon the Deep had alien dogs that are only sapient when linked into a small packmind by an ultrasonic organ, and lacking thumbs, they do a lot of their fine manipulation through mutual cooperation of their jaws, and have to avoid echo chambers or getting too close to other packs, etc.