Can you trade with Pokemon Diamond, HeartGold, etc.?
No, you cannot. You can, however, do one-way transfers of your Pokemon from your 4th Gen game (Diamond, HeartGold, etc.) to your Black or White version, similarly to using the Pal Park in those earlier games to migrate Pokemon from the GBA games. Please note you transfer them FROM Diamond TO Black; you can’t send Black or White Pokemon to an older game. Please note that you cannot do this until after you’ve obtained the National Dex and you can only do it with Japanese versions of Diamond, HeartGold, etc. via the Pokeshifter. And also note that the transfers are ONE-WAY, so you cannot get them back.
No, you cannot. You can, however, do one-way transfers of your Pokemon from your 4th Gen game (Diamond, HeartGold, etc.) to your Black or White version, similarly to using the Pal Park in those earlier games to migrate Pokemon from the GBA games. Please note you transfer them FROM Diamond TO Black; you can’t send Black or White Pokemon to an older game. Please note that you cannot do this until after you’ve obtained the National Dex via the Poke Transfer in the Poke Transfer Lab on Route 15, or if you unlock the Transfer Machine in Castelia City, you can transfer the event Shiny Raikou, Entei, Suicune, or the event Celebi before obtaining the National Dex to unlock the Zoroark and Zorua events respectively. All transfers are ONE-WAY, so you cannot get them back.