Vader probably knew Luke was on the Death Star because Vader killed Obi-Wan in sight of Luke.
Here's the relevant clip for easy reference:
Luke screams out "No!" when he sees Obi-Wan die, and he does it loudly enough to alert the stormtroopers watching the fight. Vader might have heard that. Even if he didn't, Vader likely caught a glimpse of Luke before the blast door closed on him. And it would be surprising if Vader didn't detect the Force presence of his son in such close proximity, which he later felt at the Battle of Yavin in the X-Wing that destroyed the Death Star.
Furthermore, Obi-Wan was obviously covering the escape of his friends by delaying Vader. Vader surely looked at all the security camera feeds (there was probably a camera trained on the Millenium Falcon) and saw Luke's escape. Luke's emotional reaction to Obi-Wan's death means that Luke and Obi-Wan had spent some time together.
Between Luke's Force presence with Obi-Wan on the Death Star, and the same Force presence at the Battle of Yavin, it's not difficult to put these facts together and guess that Obi-Wan -- one of the few remaining Jedi -- had helped train Luke. And since Obi-Wan died helping Luke on the Death Star, he can no longer help Luke.