I think I might be able to answer your questions too. I don't think the 2 amp trickle charger will be enough, but it depends on how long its on the charger and how long you use the car. A car uses roughly 20-30 amps while running. We'll use 30 to be more conservative. Now, if you have a 30 minute drive to work, thats 1 hour per day of constant 30A use or 30 Ah. Now you're at home and you have to regain that 30Ah. At 2A per hour, you'd need to have it on the charger for 15 hours. Thats pushing it awful close. I don't know about you, but I don't have 15 hours a day that my car could be plugged in. If your trips are shorter you may be fine. Alternatively, you could also get an ammeter and see how much your car actually uses. Keep in mind headlight, defroster, radio usage is going to majorly effect it. I'd recommend a faster charger.
If the battery runs too low and you have to kick the alternator back in I'm sure its gonna take its toll. I would think that the alternator would be working as hard as possible to recharge the battery.
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