Ok, I don't know if this is gonna be a silly question but I am very confused. A lot of times I have came across expressions such as:

"Project duration"
"Energy carrier"

My question is: when should I use this "forms" and what should be followed in order to create this expressions in a correct way; I mean, why these expressions don't go like this:
"Duration of the project"
"Carrier of energy"

This is something that I have not understand and I believe that this can help me to improve the way I speak and write english.

Thank you very much!
It is not a silly question, and it does not have an easy answer. Three of yours sound fine, but 'carrier of energy' does not, and I have no reason to offer you except that I have not heard it—which does not mean that it is wrong! I can well imagine it in some particular context.

As far as I know, there is no rule but only general practice. With time and use, the 'of' form tends to convert to the noun + noun form for its simplicity and directness, I think.
In English, it is common to use a noun to modify another noun.
The phrasing offers a shortcut to using "of the XXX." In linguistics, it is called a noun adjunct.

In your example (project duration), the of-phrase form is probably just as common as the noun adjunct form.
There are no set rules that I know of that specify when a noun can be used as an adjunct, and when it cannot.
Sometimes a phrase such as "Energy Carrier" will just be used in a business context and become popular.