Car locks the doors while driving and locks the doors when parked. Alarm beeps 2x when I unlock the door with the fob until fob stopped working now full alarm sounds when I unlock manually.

To arm content theft alarm.
1. Open the door.
2. Lock the door with the power door lock switch or
the remote keyless entry transmitter. The
SECURITY light should flash.
3. Close all doors. The SECURITY light should go off
after approximately 30 seconds. The alarm is not
armed until the SECURITY light goes off.

If a locked door is opened without the key or the remote keyless entry transmitter, the alarm will go off. The headlamps and parking lamps will flash for two minutes, and the horn will sound for 30 seconds, then will turn off to save the battery power.

Fob didn't work so the alarm immobiliser was armed and active when the locksmith opened the car - with predictable results.

Fob still not working - broken or needs new battery. Have you fitted a new battery into the fob?

The alarm immobiliser will probably remain armed until the doors have been locked and then unlocked with the fob.

There is a small chance the system can be fooled into thinking it has been disarmed by disconnecting the battery (overnight if poss) and then with the door open and the ignition key in and turned on, when the battery is reconnected it might be possible to start the engine...

your also suppose to hit door lock 2x before start and if alarm still goes off problem with fob or your aftermarket alarm programming

double posted. wow.
when it beeped, did you look in the display (RPM)
it tells you why?? the VFD or EVIC tells you why.? (rpm dial)
do you park with the alarm on , on the street or a garage?????
if in a garage park and turn alarm off. it does turn off the alarm.
did you bump the panic button?
eg its under your pillow?? LOL or the cat chewed it?
read your other post, it's got lots of answer there.
to find cause.
if the horns stays off, if alarm is off then its not the horn button.

as many will say. there are 4 things that run the horn.
button horn
alarm
door locks.
panic.(part of alarm but not totally)
on my car, i have most themn turned off, like the lamp flashings.
and the horn chirp is off on all my cars, all i get is the door lock click sounds, nice (neighbor friendly)
so turn all all that and see if the horn still fails.

that panic button can fail,
if mind did id pull the fob battery and then use FOB 2.
to see of the FOB fails.

your other post said driving
this one says, parked. 3am clue.

Sounds like the key fob is going bad and needs replaced.

You should be able to just unlock the door with the key, and even if the alarm is still going of try to start it the key should override the alarm.

battery of car is zapped of energy...not sure if alarm system to blame, after driving it for a few minutes..clock and radio display lights turn off, horn can barely be heard...sometimes, motor shuts down completely. have had to put in 2 new batteries in just a matter of 2 months?...any idea what this may be?

This does not sound like a fob fault - but a locking control module fault , either in the hardware or software of the unit. Get it checked at a Jaguar dealers. When unlocking using the key - as soon as the door is opened you should hear a chime sounding inside the car - this is a timer counting down to sounding the alarm. If you put your key in the ignition as soon as you open the door the alarm should not go off and the chime should stop. If it does not this again points to a fault in the locking controller.
hope this helps - good luck.

If the car beeps twice when you unlock the doors, it means there is a fault in the car alarm system. Usually when this happens the red LED lights on the "door lock" button on the top r h side of the dash. Also on mine, when you try to open the passenger door the window does not drop the small amount as usual, but that may be part of my alarm problem.