How much of our fossil fuels and landfills would we save by using combustible waste methods including residential trash, etc.?
Not much - there will be no math in this answer, just thoughts. How much trash do you make a day that might burn? Biological wastes have so much water in them that they take a lot of energy to evaporate out the water and therefore can't sustain a fire - think trying to get green leaves to burn. Food waste is the same issue. So what about your newspaper and the Amazon delivery box? Maybe a pound a day? Now - how much energy did you consume? Drive anywhere? 20 miles per gallon? That's 8 lbs of gasoline. Heat/cool your house? Another few pounds of some fuel somewhere (whether you used it at home, or bought electricity generated miles away). Let's don't consider that methane is used to make ammonia used as a fertilizer for your crops. Or the fuel needed to deliver that cardboard box or make that newsprint.
So even without a calculator you calculate "not much".
Most of the materials "sequestered" in landfills or dumped in Oceans or Gullies could be burned to reduce the need for burning fossil fuels. Until there is a perceived to use the resources rather than throw them away and waste useful land, very little will be done. Even where landfills are producing huge amounts of Methane, Seattle could allow use of or use landfill methane to advantage, but they to burn it to get rid of it; they do, however capture Methane from at least one sewage plant to provide power to run the operation. We are a very wasteful nation!
Q: How much of our fossil fuels and landfills would we save by using combustible waste methods including residential trash, etc.?
A: The question is how much do you wish to spend to accomplish this. It is currently done BUT the added cost is deemed acceptable by the local population that are paying more for the waste disposal than landfilling would cost them.
It is true that burning garbage for power is quite feasible. It has(or was ) done in Europe The possibility of some toxic substance being burned and entering the environment is there, but I do not know whether this has been properly researched. The main obstacle is public perception.
It's not very efficient, so the net energy savings are not very significant. The big benefit is reduction of physical mass. The big detriment is increased CO2 in the atmosphere.