Can different races donate to each other and be a match? like asians to whites?

Yes: Everyone is the same color on the inside. There are some advantages, however, in exchanges between the same ethnic groups in that they are more likely to have greater genetic similarities. This may offer some immunologic advantage and decrease the risk of rejection. We now have sophisticated tests which are much more informative that just looking at ethnicity alone.

Absolutely: Happens every day! i rather doubt anyone can tell by looking at it from which racial group a solid organ came from.