There is this 5V 4A AC DC power supply I can connect to the arduino which will give off 4A in the 5V output pin. Would having this too many amps in the circuit? Or too many amps going into the solenoids creating too much wattage? Or would it work out?
The power supply does not "push out" 4 Amps. It puts-out a constant 5V, and the current draw depends on the resistance/impedance of whatever is connected to the power supply. (Resistance means resistance to current-flow.)
Most of the stuff we work with is considered "constant voltage". For example, the electrical outlets in your house put-out a constant 120 or 220V (approximately, depending on where you live). If nothing is connected, the voltage is still present, but no current flows. A toaster "pulls" more current, consumes more power, and generates more heat than a small lamp, If you try to get too much current out of the wall (or from a battery or power supply), something will "give". The voltage will drop, something will "fry", or you'll blow a fuse or something.
Car batteries are rated 12V at several hundred amps. But if you touch a car battery, only a few microamps flow through your body, because of your body's high resistance and you don't die. However, the spark plug voltage or household voltage can be dangerous!
The relationship between voltage, current, and resistance is determined by [u]Ohm's Law[/u]. (Current + Voltage/Resistance, or Amps = Volts/Ohms).
Power (Watts) is calculated as Voltage x Current. With algebra and Ohm's Law, you can get P = Voltage squared/Resistance or P = Current squared x resistance.