Internal combustion engines, including engines producing power from solid or slow burning fuel(s), such as biological-based or petroleum-based fuels, wood, corn, biomass, coal, and waste products, and/or possibly other liquid or gaseous fluids, as well as methods for operating or implementing such engines, are disclosed herein. In an example embodiment, the engine includes a crankshaft, a piston, a cylinder having an internal cavity and several ports, and an assembly having a chamber having a first region within which solid fuel can be situated and combusted. The assembly further includes a diverter valve so that, depending upon a setting of the valve and during engine operation, first and second amounts of compressed air respectively proceed to the first region and to bypass the first region, and a combination of combustion products and the second amount proceeds via one of the ports to the part of the internal cavity.