A second or two is not long. How old are your spark plugs? How low was the battery voltage dropping during cranking?
If you suspect low fuel pressure, measure it at the valve on the fuel rail after turning the key to the on position before starting the vehicle, or for the first test, turn key to on position and leave it there for a couple seconds, then turn it to the start/crank position.
As far as heavy consumption during driving, what is the MPG you are getting? I always get terrible fuel economy with stop and go driving around town with my '98 but this was since new, with nothing wrong, often not driving it long enough to even warm up. I mean that I often get a little below 10MPG if none of it is on highways.
There is much that could have gone wrong by now, like partially clogged fuel injectors. How is your fuel quality, is it top tier (for your region) so it has ample detergents and PEA or equivalent additive in it to keep the fuel system clean? If not, adding a fuel system cleaner to 1/2 tank of fuel is something I'd try, though it may take many miles to make a difference.
I don't know that much about troubleshooting 1st generation Explorers, besides checking for OBDI codes if the dash light is on, but would consider pulling the spark plugs to check condition and see if any look different, like evidence of misfires, look for vac leaks too.
