Im helping a friend re-wire 3 new high hats in his kitchen with old existing 3 sets of 14-2 wire in ceiling,how do I make proper connections to new lights?we took readings on the wires and all of the whites are hot?any suggestions?

Probably have a switch loop that is unmarked. How many wires and what colors on the switch?

2 wires running to both switches in wall,black and white.when we connected everything in ceiling,we re-attached all whites to white and blacks to black and got hot readings on all whites.Could it be possible when old wiring was done that they could have used one of the whites as a hot and if so,would it be better if we ran a new line?

The code allows white to be a current feeder IF it is so marked. In the ceiling box should be a hot black and a neutral for the same circuit and a black and white from the switch. The white that is paired with the hot black should go to the light whites. The hot black goes to the switch white and the switch black goes to the light blacks. Put black tape on all current carrying white wires. Let us know how this works out.