Bad Company 2 Question

yes
but you can still buy it off steam which would be safer as your not entering details into an untested service.

As Hexit said, it would be better if you buy BFBC2 and it's DLC from Steam.

i can't buy vietnam from steam because I have physical bf2bc. but i can buy it from ea direct

I dont think it would work buying from different platforms, you'd need both on steam or both on origin. pretty sure it tells you that on the steam bfbc2 vietnam page anyway.