Hello bebita. I don't know if the house/garden are bugged, but I do know that Queen Noor, a few months after the arrests happened, tweeted a couple of comments that her and her grandkids (namely Princess Haya bint Hamzah) had their phones bugged. I think she maybe alluded to the fact that they found that Pegasus software had been put on their phones.
I strongly suspect that all of the family is under surveillance.
If you follow social media (esp. Instagram) you will see many photos and videos of the children with Hamzah, the kids playing sports, attending school etc. So very hopefully they are living an *almost* normal life. It's not clear if they still live at the palace with Hamzah or not. I have heard rumours on some websites (ONLY rumours/gossip, I cannot say if true) that they no longer do live at the palace with him.
And finally, my impression is that he will only be released IF the King decides he can be released. And that the King had given him a few chances and made a "final decision" to detain him indefinitely. The impression we all have is Hamzah is under house arrest for the rest of his life, unless he and the King are reconciled. (And my gut says neither in inclined towards a reconciliation).