Remote fob - battery drain?

[dvhttn]

Right. Replaced the button battery in my remote fob a couple of weeks ago. The old battery still worked but was a little swollen, as it might be after many years of service (not changed it since I got the car in 2005 ... ). New one seemed to work from further away. Fast forward almost a week and no remote functions! Second remote worked, as did unlocking manually. Another new battery went in and all was well - for a few days and the same thing again! So, 2 questions:

1) has anyone had their remote fob 'drain' batteries quickly like this? If so, did you find out why? (Batteries were "new" from Amazon recently - weeks ago, not months or years - but obviously could still be 'fake'/'very old')

2) when unlocking manually the hazards start and don't stop until I turn the ignition on. I'm assuming it's the alarm going off (but can't tell as my siren is not there .... ) but why?

Ta.