What’s the new car @swj? Any pictures?
Sorry, no idea what the grinding noise might be, but other forum members might be able to offer some suggestions. Is the noise there all the while or only under certain conditions - e.g. when braking, cornering, accelerating, or when performing other specific manoeuvres? Does the volume of the noise increase or decrease under certain conditions or with changes in speed of the vehicle?
As for the “duph” noise; I think you might be right with your suggestion that the tyres might have developed flat spots, especially if the car’s hardly been moved in six months. Are there any vibration or bumping sensations that can be felt through the steering wheel or seat? Does the frequency of the “duph” noise increase and decrease as you accelerate and slow down? If it is flat spotting, if it’s severe it’s sometimes possible to see the deformed / flattened section of the tyre.
Hope you’re able to find out what both noises are. When you do, please provide an update for the benefit of other forum members on the cause(s) and the fix(es).