well so if you can click on all songs and can download them to offline (green arrows) everything is right with your account subscription.
Now to your Problem:
on the left side of the current playing song on your mobile device there are two arrows that are crossed in the middle. If it's green, it won't play the songs in the correct order. If you click on it and it will light up white, every song will be played in the correct way :)
If this doesnt help please answer so i will continue my research :)
Good luck and have fun. if it helped please leave a kudo :)
Max aka. Amarro
If i helped you don't forget to leave a "Kudo" or "Accept as Solution".