I am changing light fixture and putting pot light. The original wiring shows one two black wires and one white joined together. The others are 2 white and 1 black. And one black an one white. Is this correct?

Most likely correct, but your description is rather impossible to understand.
It is pretty typical to see a white and black together, it's probably a switch loops situation.
What makes you think it is wrong?

The white should be marked with black tape or a magic marker.

The white should be marked with black tape or a magic marker.This has not always been a code requirement, so there is a very good chance it will not be that way.