98 Dodge idles rough. Burnin' gas way too fast. Sluggish through the low gears. 130,000 miles. V6 3.1

Put some Sea Foam in with your next gas fill up..helped my 03 Stratus (147,000) runs great

I'm sure your check engine light is on try....
https://www.autozone.com/landing/page.jsp?name=top-five-reasons-check-engine-light

The carb has a 5 minute high idle till warm. as for the running rough might try to rebuild it.

It won't shift 1-2 or 2-3 or both unless you let off? If it is just 1-2 it might be a band adjustment, but I'll bet you have a plugged governor solenoid screen also.

cause you either low on water or your heater core is half plugged

If the engine seems to run fine over 1450 RPM maybe there is a vacuum hose leaking or EGR valve is slightly stuck open. Any help from the OBD II trouble codes? Or is there simply no MIL and no stored information in the OBD II computer read at the local parts store through the connector by the drivers knee?

Then you might want to idle the low idle speed up a half a turm to see if that sovles the problem.

probable vacuum leak query brake booster

Idle is rough because not a right Air/ Gas mixture.
The ideal air /gas ratio is 14.6:1. If less than that it has rich mixture. If it more then that it has a lean mixture.
Back fire happens when accelerated because of of rich mixture pumped out at exhaust cycle is burning.
At speed above 40 miles/hour, temperature and fast compression cycle make the problem is less obvious.
Cheap first shot is to replace the air filter to correct this ratio. If it doesn't help, need Fuel distributor service. ( However people like to make easy money from you first, they will convince you for a turn up) Good Luck. I'll check back to see how the progress going.

try cleaning the throttle plate with the right cleaner . from a auto parts store.