Van missing on acceleration?

I have a Ford e350 v8 year 2002. The van has 126,000 miles. The van had sat for a while and has had some work done to it. New starter, brake lines, bearings replaced in engine, new pan gasket. Mostly on high acceleration a I get bad missing and a shutter like its not getting enough gas or something. I was concerned that it may be the transmission filter clogged, maybe the coils, or maybe the spark plugs need replaced? I'm also getting a speedometer that jumps around part of the time, possibly from sitting. Any serious suggestions or input would be helpful in the diagnosis process. All fluid levels are clean and at max.

Added (1). I did notice a burning smell the one day going up a hill and it was missing/slipping a lot. Really searching for some diagnostic ideas so i can start narrowing it down. I'm afraid to drive it to a shop with it missing like that. Closest shop is 17 miles…

What can turn on the battery light in the car other than the battery and alternator?

My car is a 96 ford contour. The car was perfectly fine when all of a sudden the battery light on dash started to flicker. When we parked the car at home and attempted to turn back on the car wouldn t start. Tried it again nexed day and at the first try car turned on but battery light remained on. When turned off and attempted to turn on again car wouldnt start. We went and checked the alternator and were told that regulator wasn't working. So we changed the whole alternator (just in case). We checked the battery and were told battery wasn't holding charge. So we bought a new one. Battery light is still on. We cleaned all possible corrosion in wires on alternator and battery but still light is on. We're at a stand still any ideas of what else we can check?