This sounds like the rubber support loops that tie your exhaust pipe to hooks welded to the bodywork are perished or one has snapped off, this will cause the exhaust to rock about when the engine moves or the car goes over a bump and can cause it to hit the bodywork. Have a look at them to see what state they're in, replacing them is only a few minutes work and you can easily do it yourself.

The speedo cable jumping is usually because it's in need of lubrication or bent too tightly somewhere. Either of these will trap the cable and cause it not to rotate smoothly, this will make the speedo needle jump.

The speedometer cable will be connected to the gearbox - this is a mechanical cable with a rotating inner cable, not an electrical one with a sensor on the end. As this car is front wheel drive any noise from the back of the car has nothing to do with your transmission. When you put your foot down hard the engine will rock and will pull on the exhaust pipe (which is why it's soft mounted rather than being bolted directly to the car), this could explain why it happens when you accelerate but not when you drive over a bump. It could also be worth checking that your engine mountings are okay, if the gear lever moves a lot when you accelerate then this is a sign that a mounting needs to be fixed. A broken mounting would allow the engine to move excessively in reaction to the force that it's applying to the driveshafts.

The air filter out might want to reason that difficulty,even if the perfect time I had a vehicle do this it became the throttle position sensor even if it became on different sort automobiles so i do not locate out about Honda's.