1-The voltage from the Arduino is about 5V but as soon as the Opto is plugged into the circuit, it drops to about 1.5v! Why?
Are you measuring at the Arduino output or the optocoupler input? The LED in the opto will drop around 1.5-2V and the resistor will drop the rest. You should still see 5V if you measure between the Arduino output and ground. If not, the Arduino can't provide enough current to drive the opto.
2- However, the Opto is still working fine since on the other side of it utilizing a 12v for now, it shows about 12 with Opto inactive and when the Opto kicks in it drops to 12(source) - (1.5 from Arduino with Opto active) = 10.5!!! Why is the Arduino voltage being deducted from the 12v source?
Where are you measuring the voltage? Across the collector and emitter of the opto? Measure between the gate and source of the MOSFET, since this is the voltage you want. With 15K and 10K resistors and a 12V supply, you should see slightly below 4.8V at the gate with the opto turned on.
3- The Mosfet is also functionin but sending just 1V to the solenoids!!!???
Once again, where are you measuring? Measure across the solenoid coil. If that's where you're seeing 1V, measure across the source and drain of the MOSFET. You should see a high voltage (near 12V) across the source/drain with the MOSFET off, and a low voltage (<1V) with it on.
Also, check your 12V supply to make sure it's producing enough current to power the solenoid. Also, make sure D2 isn't installed the wrong way. It's correct in the schematic (reverse biased) but if you install it the other way, it'll short out the solenoid coil, and probably overheat/blow the diode.
I am using a 10k and a 5k in series for the R4, that is not the problem or is it?
That's fine. Resistors in series add their resistances together.
P.S. What's powering the Arduino? The same power source as your 12V circuit? If the 12V supply can't handle the current, you'll get a voltage drop when the solenoid tries to turn on, causing your symptoms (including the low voltage at the Arduino output, if that is powered by the same supply).