"He said the one of the battery ground cables was exposed and it fried the battery so he repaired the cable and replaced the battery." That doesn't make any sense.
The +12 volt cable from the battery is close to the passenger-side tie rod. In the earlier production cars, the cable was too close and would rub on the tie rod, wear thru the insulation and short the battery to ground. But I was thinking they fixed that problem at the factory well before 2001.
You'd probably notice if your brake lights were always on, but a battery draining happens on these cars when the brake light switch gets out of calibration. Verify that the brake lights aren't staying on. If they are, we can tell you how to calibrate the switch.
How much does this car get driven? With a good battery, the normal ignition-off drain current will discharge it in about 3 weeks, quicker if the battery is old.
Can you measure the voltage at the battery with the engine running just above idle with the lights and cabin fan turned on? It should be between 13.5 and 14.5 volts (the PCM adjusts it towards the higher end of that range in warmer weather, and towards the lower end of that range in colder weather). If it's not much above 13.5 *and* it doesn't get driven a lot, the partially charged battery could drain between uses. Let us know what the voltage is with the engine running a little above idle.
Check the condition of the green fusible link branching off of the battery pos. cable near the battery. It is the connection between the alternator and the battery. It can get eaten up with battery acid if not cleaned off. When a lot of copper gets eaten away, the resistance in that cable goes way up, so the alternator can't charge the battery very well. Check it for a lot of the white battery acid residue growth.
1) Brake lights do not stay on.
2) Car is driven about every 2 - 3 days.
3) After jump starting the car, I took it to Advance and AutoZone to check the battery and alternator. Both places useless to do that, so I bought a voltmeter and watched YouTube video how to do it myself (all tests at approx. 1500 rpm's).
a) Battery with and without load 13.4 volts.
b) Alternator with load, black lead to bat, red lead to alt case = .15, OP said don't want reading over .1, if so, then you have a problem.
c) Alternator with load, red lead to bat, black lead to neg nut on alt = .35, OP said don't want over .3
4) I did not see a green fusible link branching off the battery because the pos and neg connections are below the air filter, and I did not see any links between above the air filter from the battery to the alternator. If any acid on a fusible link on the battery connections below the air filter, I'm sure the mechanic who replaced the battery about a month ago would have cleaned it. There is no acid build-up on battery connections above the air filter or on the connections to the alternator.
1) Is it normal for battery voltage to stay the same @ 13.4 with and without load?
2) Both of the alternator tests failed. If your recommendation is to replace it, is it a difficult job? I have replaced a water pump, serpentine belt, and AC Compressor / Dyrer on other types of vehicles, so I know how to turn a wrench.
3) I noticed that while engine idling, I heard intermittent sparks I think near the spark plugs. Could that cause the battery to drain or the alternator to not charge battery properly?