I had a 96 V10 dodge, also a 2000 with a 360, and drove several others in that time frame for work.
Its not normal to hold gears, it should shift like any other trans, when healthy.
My 96 with the V10, it did what you described, got progressively worse. Its the transmission. They just don't last behind either the V10 or the Diesels when works. Mine had 125k, it was on its 2nd trans, and that one was on the way out.
It'd sometimes not move right away after sitting (fluid draining out of the converter), and then driving, it'd hold gears too long or sometimes not shift at all. Have you checked the fluid levels? Mine leaked out the front pump seal and when it gets low, it'll do that worse. Checked it for transmission leaks?
Mine never slipped either, but did just like what you'd say, on the gas, it'd stay in 2nd forever. If I manually put it in 2, then shifted to 3 (OD off button pressed), it'd usually jump to 3rd, sometimes pretty hard. I would check fluid level first.
Mileage wise, I got 11mpg or so city, never drove it on the highway empty, really, but probably 12-13 there. 9-11mpg towing, depending on speed. Load wasn't much of a deal, best towing mileage I got was towing 9500lbs (tractor) but at steady 58mph. Towing my Toyota at 80mph was 9mpg or so, 9.5.
Its like no matter what you do with it, it'll get around 10mpg +/- 1 or 2.