The OP has been updated. I'm thinking of making a HM list for Asian albums, though it's been a flop.
I didn't pay attention to non-Asian music aside from my faves (and their carbon copies) this year, so I don't have much to say about the songs and I don't even know enough albums to make a top. Here is the list of the songs I've enjoyed in 2015. Some songs are universally acclaimed, some are unknown, some are hated by the artist's respective fanbase, but it doesn't really matter.
TOP 25 (NON-ASIAN SONGS)
25. Melanie Martinez - Cake
24. Hailee Steinfeld - Love Myself
23. Carly Rae Jepsen - All That
22. Marina & The Diamonds - I'm a Ruin
21. Annie - Out Of Reach
20. BANKS - Better
19. Missy Elliott - WTF
18. Zella Day - Shadow Preachers
17. Grimes - Flesh Without Blood
16. Courtney Barnett - Pedestrian At Best
15. Beach House - Bluebird
14. Carly Rae Jepsen - Emotion
13. Nicole Dollanganger - you're so cool
12. Grimes - World Princess Pt. II
11. M.I.A. - Borders
10. Chelsea Wolfe - Carrion Flowers
9. FKA Twigs - Glass & Patron
8. Lana Del Rey - The Blackest Day
7. Grimes - Butterfly
6. Beach House - Days of Candy
5. Chelsea Wolfe - After The Fall
4. Alice Glass - Stillbirth
3. Susanne Sundfør - Accelerate
2. Lana Del Rey - Honeymoon
1. Grimes - REALiTi