[Griefbringer]

As regards using machine guns in close terrain like forests, the best trick might be to keep them a bit behind the main infantry advance (so that the enemy does not have LoS to them) and then in beginning of your turn use them to Z-fire areas that you suspect to be under enemy control (especially areas that your artillery fire did not cover well enough with their barrage). Then advance with your main infantry line. MG unit doing Z-fire may not cause as much suppression as mortar bombardment, but if you just manage to pin the enemy that will seriously reduce the effectiveness of their firing. MG units usually pack plenty of ammo (around 90 firing actions worth), so they can keep on Z-firing for quite a while.

Flamethrower tanks (with 2 hex range) are also great for suppressing suspected enemy positions in close terrain - just drive into 2 hex range from a house or forest hex and Z-fire once or twice, and the occupants should be heavily suppressed. Granted, this tactic becomes riskier as the war progresses, since advancing within 2 hex range tends to expose one to panzerfaust fire.