How many days would it take to drive 2500 miles if you drove 12-14 hours a day?

It will take 33±1 hours of driving time.
see https://goo.gl/maps/M8jWjf8Kc8H2
But I would budget for 25% due to traffic and weather conditions.
leave alone the time for sleep, food, bio breaks etc

You never leave a car running, as it will
overheat the Exhaust Converter
When you run out of fuel, you sometimes
ruin the Fuel Pump
It depends on gas to lubricate it,as strange as it sounds
Check fuel pressure & volume at the motor with a gauge

check u r alternator

First question is what constitutes "overheating".
Since the car has been parked for years, the thermostat could be sticking closed.
The cooling system could have air pockets and need to be bled.
The water pump may be corroded inside and not pumping enough volume.
If the gauge goes above half way, the fans should start up. But half way should be more or less normal, not hot yet.
I would look at flow problems first, beginning with removing the thermostat and driving it without one for a few days. Also check and see if there is a process to bleed the cooling system of air.

Ever consider the Fuel Pump
may have failed?
Put a gauge on it and road test

My recommendation is to have the problem fixed before it turns into added expenses of towing, possible overnight hotel bill and food on the road....

Running so few miles has accelerated the aging of the battery - the battery never had a chance to fully recharge in such small trips -  so now you have to replace it a year sooner than usual.
Just replace it.

draw a small amount of fuel about 1 quart in sutable container and let sit then check for water.It will seperate in the sutable container

You've made the correct decision. Let the dealership diagnose the issue. They'll tell you EXACTLY what the problem is and what's needed to fix it (parts, labor, tax, time-frame, etc.).

THE STARTER IS GOING BAD