You can replace a vehicle almost immediately after your case is filed. You may have a limited number of dealers who are willing to work with you until after your case is discharged (about 3.5 months after filing), and you won’t get a great interest rate, but you can buy a car.
You likely will have to wait for 3 – 4 years to purchase a house. The guidelines for mortgages change frequently, so this is not a “one size fits all” situation. You have a chance after your bankruptcy to improve your credit score by making sure your credit report is accurate and by using credit wisely.