NavList:

Here's my personal take for Question 1, for whatever it's worth:

The Air Alamanac "gets away with" its P-in-A tables because each one is custom-made for the average HP of that particular half-day (the P-in-A value for 0 altitude, i.e. on the horizon, is the horizontal parallax).  If you flip through the pages of the AA you'll note the tables change from day to day, and even tables that apparently have the same HP value (to the nearest 1') can have different critical points as the tables are calculated at a higher precision and then rounded at the end.  The tables in the back of the Nautical Alamanc are meant to cover all possible values of HP throughout the year.

And yes, the "weirdness" in the upper portion of the Lunar Correction Table in the NA is because the table combines refraction, parallax and semidiameter into a single table.  These are three separate corrections in the Air Almanac.  The Sun Correction Table does the same thing, using an average SD for the particular half-year and the sun's constant (to sextant precision) HP of 0.15'.