1. I intend to buy a new car.
2. I am going to buy a new car.
3. I'm buying a new car.
When [STRIKE]do[/STRIKE] can/could/would/should I use these three [STRIKE]expressions/future tenses?[/STRIKE] sentences?
Use sentence 1 when that is your intention. You plan to buy a new car. You are not giving any indication of when you plan to do this.
Use sentence 2 when you have definitely decided to buy a new car. Again, you are not giving any indication of when you plan to do this. (Note that it could also be the answer to "Where are you going?")
Use sentence 3 when you are at the car dealership and are in the process of making the transaction.
Note my corrections above. Please number sentences when you give us options. Remember to end every sentence with one appropriate punctuation mark.