Do not know about PrE (BM's site might define whether it works - only mentions FCP and PrPro), but PrPro works with the BM cards, so long as the BM CODEC's are updated.
Premiere Elements generally doesn't work with capture cards because they usually capture video to a codec incompatible with DV editing.
What kind of camcorder are you attaching to your capture card? We can likely recommend a better method of video capture or downloading, one that produces files that are compatible with the program.
>using black magic's software and import
If you are able to create a standard DV AVI type 2 file with 16bit 48khz sound, that will import (this is for SD video)
For HD video, if that is what you are using, you will need to report back what CODEC is used with that card
I use the card to capture analog video source using VCR that play VHS tapes
The best solution for capturing analog video is a DV bridge.
Unlike capture cards, DV bridges capture your video as DV-AVIs (as John recommends above), which are perfectly compatible with Premiere Elements.
More information and recommendations for DV bridges can be found in the FAQs to the right of this forum.