All they did to have multiple missions on the same map, was have everything already there, and you just switch ownership of units/structures via scripting. While you can create units on demand you can just place everything, then use the triggers. I'll have the commands down momentairily for you.
To change ownership...
Create Trigger, we will call it Example Trigger for this.
First, you will want to create an Event. For this, we will give the player 2 Ghouls for reaching a location. For this, we need to create a "Region." Go to Layers Menu, select Region. Create a small region in where you wish the player to be. Name it "Trigger Giver" or something discriptive for its purpose. Simply you can just go to "Unit - Unit Enters Location." Set this to the REGION. Alternatively, you can specify a unit, in this case usually a hero. However, its simply easier to use a nonspecific unit. To force a specific unit, use the Condition option, however you can just leave this section blank.
The last you want, is what its action will be. Set it to Unit - Change Owner. Set the unit (can be a structure) and give the ownership to the player you want to have it. Screenshots of this order are below.
To modify individual units, just use the unit modification menu! Reread the post, but I'm not deleteing the above at this time (unless asked to)
To do this... Select a unit.
At the very top, you see several lines named "Art" Change it to something else to change the associated picture (such as a lynx. It must be a valid file.) You will want to create an icon (as this is simply how War3 works, if you use the basic interface.) I'm not a graphics artist, if some one can provide the images, I can work it in for you. Its the Object Editor.
Your Pig Peasent.
Ah hell, I really need to learn how to read.
Theres your next level.
While I have messed around with the editor, I by no means have the skills to do any art work, and I have no idea how to change the tile set and projectile animations (I imagine via the unit menu) As for the ingame screen, I have no bloody clue how to change the resources from wood and gold to "Common and Rare", nor do I have any idea on how to make beacons work. I'm not a programmer, I just know how to work their triggers, and what to look for. I can make the units alright, thats not difficult. (Except for the ESG and EMP, those work in a method I do not know how to emulate. EMP maybe by using the same spell as the Sleep, but changing the resulting animation)
I also do not have the time to do the work for this, between school and my job, I don't have a huge amount of free time. And I've now edited this post 6 times! I'm done with this tonight.