Hi Camilo,
"Bring to life" means that you have taken a lifeless object and added life to it. The phrase is used when you want to describe someone who takes a conceptual idea and makes it a reality.
The sentence "Enterprising students can bring an idea to life" means that students can create a real product from a theoretical idea.
"Give to life" is incorrect, but "Give life to" is good. This phrase can be used in the same way as "bring to life", or you can use it to mean that you are reviving something that is dying.
"Enterprising students can give new life to existing ideas." This means that students have improved ideas that have already been attempted.
"Enterprising students can give life to an idea." This means that students have made a conceptual idea into a real product.