You're in santa barbara so i think there are AUTOZONE's everywhere, at least in so cal there is

take it to AUTOZONE and they can check your battery and your alternator while its still on the car. what a systems test does is, it read the voltage of your battery before, (it should not be below 12V for normal readings) and then they run your car above 2k or so and it should read right around 14V.

and for the corrosion, just take some vaseline and put it over the posts to prevent it. or just grab a small pack of the anticorrosion lubricant at autozone for like $.99