Q: My car feels like the tires aren't really gripping the pavement

Hello. You are likely experiencing a suspension failure of some type. The steering and suspension components are very closely related. These will interact and effect each other greatly. Due to your symptoms including excess bounce, you should start by looking into your shocks. Your shocks play a huge role in how much road disturbance you feel inside of the vehicle and may be to blame for your bouncy ride. You can perform a vehicle bounce test on the suspected corners of the vehicle to help assess this. You may also want to check the control arms. If the issue is not predominant while performing these inspections, you will want to do a full inspection of all suspension and steering components.