You don’t say what model or age of X100 you have. Mine is a '97 so that’s what I know about. The 4.2 litre cars may be different.
I have had a very similar problem which seemed to be due to the Security and Locking Module thinking that the alarm was set when it wasn’t. The clue here is that the red light on the shifter panel flashes.
I also discovered that it is quite normal for the alarm to sound after 10 seconds if you have locked and unlocked the car using the key in the door. Mine makes a quiet bonging noise and if I don’t put the key in the ignition within the time the alarm goes off.
Another thing that I discovered was that it is impossible to programme the fobs using the ignition on/off or headlight flasher sequence, that is described in many places on the internet, if the SLM is unco-operative because you can’t get the system into learn mode. If you scan the modules you may find that you have P1260 fault code in the Engine Control Module which can’t be erased in the normal way. This is a security or tamper code and it only disappears when everything is normal.
After many attempts, this is what worked for me. First sync the ECM and the Body Processor Modules using IDS. Then, erase and re-programme the fobs using IDS. I think that you will only be able to do this using the Jaguar diagnostic system - nothing else worked for me.
Next, using one of the now working fobs, unlock the car which tells the SLM to disarm the alarm.
Finally, (if your car will start you don’t need to do this but at this stage mine wouldn’t crank) using IDS erase and re-programme all the keys you have.
After I did all this, everything worked correctly and has continued to do so but I could not find a way of doing it without using the Jaguar IDS. I think there may be proprietary programmers that can also do it but I found that I needed to go through this whole sequence to get the modules talking to each other again. I hope that helps.