Is it possible to download iTunes to a portable USB hard drive?

"iTunes" is the application itself and cannot be moved. I think you mean the iTunes Library. Also technically you mean upload, though "copy" would be a better term in this case.

Apple's 6 pages of exhaustively meticulous step-by-step instructions: How to move your iTunes library to a new computer - https://support.apple.com/HT204318 Use this if you suspect any of your media are not in the standard location (iTunes Media folder).

My one-sentence summary if you always use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its sub-folders and files) intact to the other drive, hold down the option/alt key (shift on Windows) while starting iTunes, and when requested to select a library select the iTunes Library.itl file in the copied folder (Open a different iTunes Library file or create a new one - https://support.apple.com/HT201596).

Depends on what exactly you mean by "iTunes".

If you mean the iTunes Application, then no.

If you mean the iTunes Application installer package, you can copy it to an external hard drive and use it to install itunes on another computer.

If you mean use your iTunes media library (songs, movies, etc...) stored on an external hard drive, then yes.

You can read this user tip to make an iTunes media library portable and move it to an external hard drive:

Make a split library portable

Car players are all different. It is best to read the manual. Sometimes it is enough to drag the tracks from iTunes to a flash drive (I presume that is what you are using rather than a full size external disk drive) showing in Finder. You do not need the full library with all the support files (A good reason to make sure you provide all the information when you ask a questions since we were answering the question you asked, not the one you intended 😉 ).

O.k, that's entirely different.

The first thing to do, is read your car's media center manual and find out what formats it supports for the media files, and whether they need to be in a specific folder in the usb drive, or simply on the root of the drive etc...

Not all car media centers work the same way. Once you know how the media center expects the files, you can then move them onto the USB drive.

Generally speaking if your music in iTunes is in mp3 format, you could simply drag and drop them from the iTunes window onto the usb drive in Finder and see if your car will pick them up and play them.

Note that music tracks obtained from the Apple Music subscription services are DRM protected and will not play outside iTunes.