I think the alarm is a feature of the second generation car. Some people suggest that it is the spiders tirggering it. If they are not, then you need a very good auto electrician to find a solution.
If your new battery has the same technical specification as the old, you should have not noticed any side effects. I am not sure if the new battery is too big for your car and that triggers a heavy charging mode that needs all this extra power that reduces the idle speed.