How can I track/login to stolen MacBook Pro My MBP got stolen in January 2017 and is not shown in Find My iPhone but I just found out that it shows up under signed-in devices in iTunes with the serial number and the first name of the new user (Aleksej). 

Is there any way to track the MBPs location with the serial number or the sign-in information?
No

Unfortunately, There is no way to track it to an accurate location without Find My iPhone enabled. If your able to get the devices serial number your best bet would be to file a police report at your local police station.

If it was stolen back in January odds are it has already been erased and/or resold. So even if there would’ve been a way to track it, you wouldn’t be able to anymore.

Edit 1

If you enable 2 step verification, if the thief tries to log into you Apple ID on the stolen computer, it will show on your other devices an authentication code for that devices, aswell as the location of the device that is requesting permission.

So if the thief tries to log into your Apple ID and you have Two Step Verification enable, it will show you the stolen devices location.

Apple cannot track your device as it would most likely violate some privacy policy, though if you give them your consent they might be able to track your device. I would suggest you contact them and see what they can do.