The Internet Computer does work differently: A canister smart contract runs on a so-called subnet consisting of a set of nodes/replicas. The (decentralized) Network Nervous System (NNS) determines which replicas are part of which subnet. Since all replicas together ensure deterministic execution and state transition, they are responsible for both execution and validation. However, there is no “deposit” of ICP. Each node is associated with a node provider, and node providers get rewarded, in ICP, for each node that contributes to the Internet Computer.
If you’d like to learn more, you can find a technical overview here.
Let’s go over your bullet points:
Technically, each replica (running the canister) runs a BTC relay, which interacts with the Bitcoin P2P network and provides the necessary information to a Bitcoin system component (running on each replica). This component makes Bitcoin-related functionality available to the canisters.
Correct.
Correct.
The replicas running the canister jointly control the private key. And yes, two thirds of the replicas must provide a signature share to construct a valid signature to move Bitcoin to another address.
Regarding your other questions, as they pertain to the threshold ECDSA feature, may I ask you to post them on the dedicated thread? The guys there will certainly be able to answer your questions in great detail. 