Hi.
With the latest version of premiere you should theoretically be able to export an aaf which avid can import. The media will show up a offline, but using MCs ama you should be able to link to the movs, and then batch import the tiffs and targas.
Avid, when not using AMA, does an actual import. Unlike FCP or Premiere, which really just “link” to your media, Avid as you say, transcodes it into MXF or OMF – the file format on which Avid runs.
That is why it asks for a resolution. 1:1 or 1:1 10bit will be fairly “lossless”. If you’re working in HD, then DNXHD 185x or 220x will be a very high quality compressed HD format.