Hi Sharktail,
You can store your iTunes library on this HDD, but I can't tell you if your car will recognise the music correctly if it is stored in the iTunes structure. Also, your car may not be able to recognise such large hard drives. Most are only designed for smaller USB sticks or smartphones.
You can show your iTunes library under Finder -> Preferences -> Sidebar -> Music.
Actually, any hard drive should work with Mac OS. The operating system should not generally limit its use.
Formatting may be necessary for writing, but this can be done in any case. Otherwise, you can return the hard drive saying that the product description is not correct.
No, that is not possible. The adapter mentioned also requires a TB connection. Without a Thunderbolt connection, this hard drive makes little sense. You can operate it via the USB-3 connection. However, it is not worth buying the more expensive Thunderbolt version.
Yes, as you can see somewhat awkwardly in picture 4, the hard drive has a USB 3.0 port in addition to a Thunderbolt port. So you can easily connect it to your Mac or PC.