t lists a max gate threshold voltage of 2.5 volts, so the 5 volt output of an Arduino pin should be more than enough voltage to saturate the MOSFET if I understand correctly.

No the gate threshold is the point where the FET just starts to turn on. What you need to look at is the voltage quoted when the resistance from drain to source is quoted. That is the voltage you need to supply to the gate.

@robtillaart where is the

i need to do pwm nad make the random signal sinusoidal.

bit?

Good luck. Just dont let them get the better of you, okay?

Assuming that the "them" you mean are the people telling the OP to learn something so he can crawl before trying for a moon shot I think you are wrong.

No one is trying to "get the better" of anyone. Unrealistic goals only leave you frustrated and learning absolutely nothing. Much better to learn something solid and transferable than to waste your time.

I am sure an intelligent person could figure it out easily

No, many many people have been trying for years to do this sort of thing with very limited success.

but I am in 9th grade and for that I have a VERY low budget.

I have no idea what age that makes you ( I live in the U.K and it means nothing to me ). But without test equipment and knowledge you do not stand a chance. Note knowledge and experience are not intelligence, creativity or flair. But all five are needed for your quest. So start off with something that you can do an learn from that.

If you power the shields in parallel they should be fine off one adapter?

Only if the adaptor can supply the required current and the supply decoupling is enough so you do not have a ripple problem. But otherwise yes.

Your requirements are no at all clear.
Where is the arduino in this setup?
If you have a transmitter what is controlling it? PC, arduino or you pressing a button.

i think to attach one module (the transmitter) on a digital pin (configured as an output) that sends for example the number "87746"; the receiver on another digital pin (configured as input) that recieves these byte,

That makes little sense. For a start a digital output does not send numbers only binary values. And why have one pin send something and another receive something on the same arduino?

Draw out a block diagram of what you want to make it clear in your mind.

But as I said, if I just want to read from analog input and give it as output for now

Read with analogue read.
However outputting is not so simple as the arduino has no analogue outputs. The options are to use the PWM output
http://www.thebox.myzen.co.uk/Tutorial/PWM.html
Or to fit some sort of external D/A converter.
The arduino has a very limited amount of memory to store sounds there is only 2K of this memory in total for everything. That is only enough for a fraction of a second.
That link is the best there is at the moment. Try and understand what it is telling you.

Have you got the wav files in the correct form in terms of sampling rate.
Try this file and see if you can play that.

Many compiled languages use range checking, including Java(compiled), C#, Basic(compiled) and so on.

Have you noticed that you have to put compiled in brackets next to those. They are all interpreted languages that have been bodged.
Run time array checking is a severe handicap to any language especially in a real time environment like the arduino.

I want to understand if I make all the components 0603 package size, will I be changing more than I realize?

The size 0603 only applies to components with two terminals like resistors, capacitors, diodes, LEDs and inductors. It does not apply to transistors, FETs or much else.

Any ideas why serial monitor is not working?

This forum is very poor at mind reading. You have to help us.

I have set the serial to being in the sketch,

OK so post it ( read the how to use this forum sticky post to find out how)

The sensor is working fine

How do you know this?

but i have to just guess the light values to get any sketch working

Wow, you make a guess, you don't do anything else but guess and you code then works. As you have a mind reading arduino no wonder you thought we could read minds, sorry we can't.

provide signal to an polarization scrambler.

What is this? Link please.

1st. i need to randomly generate 0 or 1 (square wave).

Do you mean the times of the signal need to be random or that the appearance of this wave has to be random?

 

2nd. i need to do pwm nad make the random signal sinusoidal.

I understand all those words but that makes no sense. What do you want, please explain properly.

I found some lcds are serially enabled,

Yes they have a special circuit on them to convert the data from serial to parallel. This is normally a small processor like the arduino.

How can i make my LCD serially enable?

You don't want to do that because there is only one serial port on a Uno and that is used in uploading sketches. If you want to use fewer pins then look at using the I2C bus and an I2C port expander. Read this:-
http://playground.arduino.cc/Code/LCD

If you want help then ask a proper question. Also post your code correctly.
Read the how to use this forum stick post at the start of this section.

what state the arduino analog PWM is in when it is low,

I think you need to read how PWM works, it is a digital output not an analogue output.
http://www.thebox.myzen.co.uk/Tutorial/PWM.html

Glad you got it working. 
I was going to go through some fault finding today but it seems you didn't need it. I have been a bit busy over the last few days with a reunion of people I used to share a flat with at University, we had not seen each other for the best part of 40 years. It was a very odd experience seeing that they had all got a bit old.