Problems with syncing iPod Classic 160gb 7th gen

I had an iPod Classic for about 5 years, it worked great for me, but after a while my hard drive got fried. Now I have a 'new' iPod Classic from my friend who doesn't use it anymore, but so far it's been a pain in the ***.

What is the problem?

I don't get my iPod to be synced properly. I use a Macbook Pro late 2011 which usually works fine. I have a big music library with almost 40.000 songs. To get them on my iPod I always had to get them to a lower bitrate (128 kbps). That didn't work for me, syncing crashed my iTunes multiple times. I read that you can troubleshoot this by turning the function off. So I made my library shorter and I successfully synced my library to my iPod.

Now the next problem occurred. All the songs show up on my iPod, but a lot of songs skip when I try to listen to them or make my iPod crash like crazy. This wasn't good enough for me so I tried to check the hard drive via Diagnostic Mode (no problems there) and Disk Utility in OS X. Disk Utility gave a few errors so I decided to format the drive in extended journaled.

On to the next problem. When I formatted and reset my iPod whit Disk Utility and iTunes I was able to sync the library, but after the sync and unplugging the iPod it says it has no songs. This is really weird, because the drive is fully stocked whit songs, but the iPod clearly doesn't recognize them as music files.

I also tried to format the drive on a Windows 7 and 10 machine in exFat, but I got the same 'no songs' issue.

Does any of you have any idea what I should do? I feel like I tried everything, but the problems keep piling up.

(I read somewhere that it could be a battery issue, but I have no idea)

Thanks in advance