Amber is very submissive to Forge, because of the imprint put in her brain by Elden, who Forge happens to resemble. However, during the power outage section of Perilous, she becomes very assertive, ordering him around and ignoring his wishes not to get his injured leg treated. This seems out of character, but remember, it's dark: she can't see his face! This is Amber's real persona, unhampered by the imprint. When they enter the park, where people are gathered with lights, she becomes submissive again.
The Hive clearly treats the privacy of its residents as paramount, which is why Amber is necessary in the first place. This may be necessary for the mental health of the people in the Hive - living under the constant surveillance the Hive could create would be absolutely stifling. (It may even be a requirement of Joint Hive Treaty Enforcement.) Their systems must be designed to maximize privacy, as many cases could be solved much more easily with even modern systems - there is no way to track down the location of a given dataview, for example, which would have made finding Forge in Borderline trivial. For comparison, tracking down a modern cell phone to (at worst) 'within X distance of Y tower' is quite easy, but the Hive can't even tell what zone a given dataview is in.
In Adversary, some of this is explained - Hive England doesn't use cameras because it weakens the belief in nosies. Telepaths are more effective at protecting against 'wild bees' than cameras are, but there aren't enough telepaths for them to truly catch everything. The widespread belief in nosies keeps many Hive citizens on the straight-and-narrow. If the Hive used cameras as well, it would suggest limitations on nosy abilities or effectiveness.
Fridge Horror
Amber can't read Elden's mind because he's from Hive Genex and they speak a different language: even with him having a language imprint, she can't understand his actual thoughts. Okay. But then, why would Genex go to such lengths to kidnap her? Surely she'd have the same trouble with their citizens? Since telepaths can't be imprinted without potentially damaging their ability, how could she be of any use to them? I see two possible answers.
They can imprint telepaths without risk, or have some other way around the language barrier. Possible as they clearly know more about telepaths than Amber's Hive does, being able to identify Amber at a young age.
Alternatively, she's not much use... as a telepath. As a carrier of telepath genes, though, it's a different story. Given what they seem to know about telepaths, Genex may know how to ensure her kids will be true telepaths. So, yeah. They planned to kidnap Amber to use her to breed more telepaths. Already Fridge Horror given she'd be an eighteen-year-old captive surrounded by people who don't even speak her language and clearly don't even care about their own people's welfare. Then you remember that with the imprint, she has the mind of a three-year-old. A three-year-old conditioned to obey her handler/ abductor without question. Gaah.
We find out in Borderline that Hive Genex succeeded in kidnapping three people before Amber, one of whom turned out to be a borderline telepath. The three kidnapped people were then put in the duty child programme, and had multiple children, one of whom turns out to be a full true telepath. So they were very likely to use Amber for breeding purposes. And as an extra bonus, all the children of the kidnapped people are bilingual, fluent in (presumably) English and whatever language Hive Genex speaks. And there’s a chance all could be sent to Hive England.
Discussed further on the WMG page, with the theory that they didn't expect Amber to be a telepath, she was just the first descendant of Claire to grow up at a low enough level that they could get away with the kidnapping.
Did Keith use the time he spent with Olivia to sabotage her attempts to fight off fragmentation, as a way to strengthen his own position? Sapphire blames it on the attempts by the other telepaths to help her, but it's possible that Keith was working against them, making matters worse. He claims to care about her, but he's clearly not beyond lying about that.
