IPhone – Spilled vinegar on iPhone earpiece

This can happen when the contact spring inside the headset jack is loose, cracked or broken, or maybe the plug or jack is just dirty and shorted out. Perhaps try cleaning/degreasing the plug and then blowing out the jack with compressed air. If that doesn't work, a visit to the Apple store is in order.

This same problem can happen on different models of other phones as well, any phone that has a headset jack.

You're discovering the joys of noisy electrical grids in cars.

Do I need an amplifier?

Nope. You need a filter.

And filtering noisy car electricity is...tricky. You can't just create new, separate paths to ground because there aren't a lot of choices for where ground is in a car.

You can try putting a simple choke filter on the line between your player and the input to the stereo. That's the cheapest and easiest way to try and fix the problem. Something like this is sufficient.

If that doesn't cut the noisy you need to filter the power. Finding one of those car DC to AC inverters with a built-in USB port is likely your best bet. Something like this is what I'd suggest you try if the choke doesn't help.