In Deathwatch I notice there are rank tracks for general space marine, deathwatch, and specialty. When you are rank 1 are you eligible for buying abilities from rank one of all three types?
Yes. From the sidebar "Chapter Advances and Deathwatch Advances", page 57:
"Deathwatch-specific Advances can be selected by any Deathwatch Space Marine of the appropriate Rank, and Chapter-specific Advances can be selected by any Space Marine from that Chapter of the appropriate Rank."