273 rocker arm adjustment

I wouldn't worry about the notch in the end of the rocker arm shaft. Seen enough of them notched incorrectly. What is important is that the oil holes face down, and down in the correct direction (more "vertical" than the hold-down bolts). See diagram below, which is from the factory service manual.
0900c15280052823.gif

And yes a hydraulic lifter's internal piston must freely move up/down.

Hydraulic lifter's preload needs to be adjusted via adjustable rocker arms, or by getting the exact length pushrods which provide the proper preload in your particular engine assembly. And unless it is original/production, they will almost always be a custom length pushrod. This problem is eliminated with the adjustable rocker arms.

Once you get some new pushrods, fix or replace your stuck or damaged lifters, and fix the rocker/spring clearance issues, follow my instructions, previously posted in this thread, to adjust the rocker arms.