New 04 AWD Owner

Just bough an 04 Express Conversion van. Only has 2,000 miles on it, sold as new from the dealership. Couple of strange problems so far:

1. Battery seemed to be dead after driving it home. Put a charger on it and seems to be OK so far.

2. Side doors rattle. I looks like I may have to adjust this. Any advice?

3. Driving home in wet conditions the other day, the door locks started cycling every couple of seconds. Not sure what is happening here.

I'm getting 15 mpg on the highway, I was hoping for better gas mileage. Put some synthetic motor oil in it and will drive at 70 mph and check consumption again.

Very easy to change oil and filter. I would like to put a larger oil filter on, the PF44 and PH3506 seem small.
Also put snow tires on (Bridgestone Blizzack), 235/75R16. I guess that this is an "E" rated truck tire and has stiff sidewalls. I was hoping to get a smoother ride. Tire pressure seems to be over 43 psig. I'll check with the tire shop to see what they recommend.

Thanks, glad to see this Forum!