Will a car´s computer lose its program when the battery dies?

No. It will need to relearn the idle speed but the programing stays. If you don't go to the dealer you may miss important updates that most manufacturers have which take a few minutes. Open recalls are done for free.

The PROGRAM, NO ! the settings and last used info, yes, You can check any Check engine lites by disconnecting the batt for 10 seconds, if it comes back you DO have a problem. BEST if done at NOON/ midnight, the clock resets to 12:00.

No it will not. That would be a very bad design. You may lose, briefly, some minor data related to shifting, or radio programming or seat positions, etc. The engine can relearn most of this, but other stuff might have to be reprogrammed by the driver.

The computer loses info and then whent the battery is back up it tends to reset itself and adjust the settings after everything is running normal again.

NO but the radio will loose it's set channels. Your first two answers came form another pair of Yahoo non-mechanics who never changed a battery in a car.

Yes. Its the power from the battery that keeps the computer 'in tune' to your car.

Dead battery and the computer loses its set programme.

when the battery is recharged the computer can be reset by submitting the correct code.

theBax says it correctly. You do not lose any ecu program. You do have to drive it a bit for it to relearn your driving. And any Check Engine Codes will be cleared (except for hard codes).

No, but jump starting and putting the cables on the wrong terminals can cause a problem.

yes