My two cents...

1. Getting there - is there a good way to use the train? I can walk to the "Coaster" from the new house. What if any times are bad for driving?

I'll ditto KSAN's comments here. I don't live as far north as Carlsbad, but many of my friends who live on the 78 corridor go to SNA for flights instead of SAN. Particularly with the toll road, getting to SNA can be substantially easier.

2. Parking - If I do drive where is the best place to park - Company paid. Any secrets here?

There are many garages and privately-run lots in the area, in addition to the $18/day parking directly at the airport. I park at the Aladdin lot a few blocks away -- their shuttle service operates frequently and the drivers are fairly pleasant and helpful. [Their website is here.)

4. I will be flying to SJC as well as everywhere else, does AA use a different terminal for Eagle vs. full size birds?

Everything except the flights to LAX are in Terminal 2. This includes the flights to SJC, although AA exclusively flies American Eagle from SAN-SJC these days.

5. Am I still better off driving to LAX (1.5 hrs) for my international travel to Europe and Asia?

I can't imagine that it would be easier than taking the AE flight from SAN-LAX first. There is no elite security line at the Commuter terminal, but the wing of the Commuter terminal that has the AE flights only covers UA's flights to LAX as well. The longest security line that I've ever had there was maybe 6 or 8 people deep. Be advised that once you're inside security you only have a snack bar and a newsstand to spend your money at...there are no bars or restaurants or the like.

One other note is that in my experience, adding the SAN-LAX leg to your journey is negligible in terms of price difference (well under $50, often $10 or so).

Regarding Carlsbad, as KSAN said, AA used to fly to LAX from there and it was great. Now it's only UA and America West (to Phoenix).

Welcome to San Diego!