Rally Race with no headset

You can set your L3+R3/LS+RS to eat a snack which recovers a small amount of health (~5%). You cannot use this action if you are out of snacks. You can also do this through the action menu (hold select).

As a side note, you can buy snacks from gas stations/convenience stores (the ones you rob) if you go up the register and hit right on the dpad.

There could be a few reason for this.

First, make sure that the race is configured to allow custom cars. The lobby's host can disable custom cars if they want. Though typically, I don't run into many lobbies with customs disabled. I am level 70+, so I end up in lobbies where most people have custom cars of every type. It may be more common for customs to be disabled in lower leveled lobbies.

Second, it could be a timing issue. After you buy a car it takes a few minutes for it to be available in your garage. If it hasn't been delivered yet, you won't be able to race with it. I've also seen it take a while for purchases to propagate though their cloud servers. So it could be a case that the session that the race lobby lives in doesn't know about your new car yet. I wouldn't be concerned unless it's not available by the next day.