Facing the engine.

With the stock oil cooler.

Is the input (hot) on the right or the left?

Doesn't matter for the cooler. Don't know if the lines are long enough to swap 'em though:)

I'm installing new lines, cooler and oil temp gauge. I'm going to T into the hot line for the sending unit. Trying to figure out which is hot.

If I am interpreting the Helm book correctly the oil flows out the more rearward - lower port and goes to the cooler then returns to the engine via the more upper and forward port.