There is only the one alarm siren which is mounted at the rear right of the engine bay as you stand in front of the car - it has its own back up battery to prevent thieves from silencing the alarm by disconnecting the main car battery. Where the back up battery is 100% charged, it can run the alarm continuously for two or three days!
The clicking noise will be from the alarm still trying to sound (it is probably damaged or waterlogged, or the back up battery has now become discharged and not providing sufficient power to make the siren sound) and will probably need to be replaced.
If the fob button will not operate the central locking with the car battery fully charged, it is likely that that either the fob battery is flat (or not inserted correctly and not engaging the contacts properly), or there is a fault in the SCU - either water ingress has damaged the radio reciever circuit, or the flat car battery has led to damage or memory loss within the SCU. If the fob is not communicating with the SCU to work the central locking, it won't be able to turn off the alarm system either.
If the problem is the SCU, you will need the assistance of a specialist and I would recommend contacting technozen for advice (https://www.technozen-electronics.co.uk/
You may find the following thread useful to help diagnose possible SCU problems and assist with its removal if necessary: Pektron SCU/BCU
Am I right in thinking that you had a new car battery back in February? - I would be surprised if it has expired already tbh, so I think the battery running flat in only a week may be due to a parasitic drain - you would need to disconnect the battery negative lead and put a multi meter between the battery negative terminal and the earth lead - you shouldn't have more than about 30 milliamps with all the car electrics switched off. If it is much more than that, you will need to find the culprit by a process of trial and error (disconnect electrical components individually and check for any reduction in the drain). It could be the radio, a stuck or faulty door switch (or bonnet switch) among other things, or even damaged wiring causing a short (check the tailgate loom for damage as well as the engine bay wiring; although such wiring damage usually gives rise to other more readily apparent symptoms).