It sounds to me that this engine is very old and not very well maintain.
The reason why your RPM drops when you tap the gas pedal is because the instant you open the throttle plate, the air enters the engine is faster than the fuel that your fuel injectors can provide. Due to that your engine is running a lean A/F mixture, so lean that it makes a noticeable difference and it might cause the engine to drop it's RPM or just die. It is the same reason why you feel power loss when you step on the pedal. This sudden change in A/F ratio also causes your ignition system's resistance goes up due to the lean mixture inside your cylinder. Once the fuel can "catch up" with the air that enters your engine everything goes back to normal.
You might need to adjust the Fuel Pressure Regulator to a proper level, clean your fuel system and fuel injectors and change your fuel filter.
If you want to check what engine it is, just open the hood and look at the engine number located on the engine block, some where on the left side of the header if you are standing in front of the bumper.
Check the back up light's light bulb and see if it's burnt.
I don't even want to get in to how to rebuild your wiper motor and stuff, it's probably costs less if you just replace the whole thing or find it off ebay or something.