The ledger spawns an archive by calling create_canister with the default canister creation arguments. The default freezing threshold is approximately 30 days.
When a ledger spawns an archive, the controller of the newly-spawned archive will be the same as that of the ledger. E.g., for the ckBTC archive, the controller is the NNS root canister, the same as the controller of the ckBTC ledger.
Making sure that the ledger and archive canisters do not runs out of cycles and get wiped, is nothing specific to ledger suite canisters. One way to facilitate the management is to use a service such as CycleOps.