put different colors on each layer.
if you need a whitebase... that's additional layer.
so if you have total 3 colors on your artwork, you should have three layers in your file.... plus a whitebase so total 4.
yes, illustrator is good...and photoshop too. or both combined.
space (or overprint) for ink spreading will depend on the thickness or thinness of your ink. you may want to make trials before going to production. another variables to consider are the kind of t-shirt you will be printing on and how tight the color spaces in your design.
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