choking up and lie angle

Yes, the effective lie would be 1 degree flatter and swing weight would be approximately 3 points lighter

Yes, for every inch that you grip down, the lie angle will be flatter by one degree. Plus, gripping down an inch or so generally gives you more control with a very minimal decrease in distance. Usually, the decreases in carry distance are mainly in the short irons.

For every 1/2" you choke down you loose five yards, according to one of the PGA pros I play with.

Since golf is not a game of absolutes, except for your score, your pro can certainly use that as his guideline. As I previously stated, the decreases in carry distance are most noticeable in the short irons. Said another way....gripping down an inch or 1/2 inch on a 4 iron will not make as much difference in your normal carry distance as doing the same thing with your 9 iron. Plus gripping down on a long iron will generally offer enough additional control and accuracy to offset the slight decrease in carry distance.

I have struggled lately to get a solid divot. Most likely coming up and out of the shot (or my arms are shrinking); however, this trend has me wanting to add 1/2" to the standard length of some new AP3's.

What effect should I expect by adding a 1/2" to the standard lengths ? I'm leaning towards the AMT Black S300's.

One more question about the shaft length and lie. When you say choking up would produce "1 degree flatter", does that infer a 1/2" longer shaft would bring the toe up a little ?

To clarify my comment above +/- 1/2 inch in length = +/- 1 degree in (effective) lie angle as well as a +/- 3 swing weight points. The effective of shaft length is proportionate e.g. an 1/4 inch decrease in length = 1/2 degree decrease in effective lie angle and a 1.5 point reduction in swing weight.

Please note the swing weight changes are approximately as the final effect is influenced by the weight distribution of individual shafts- the difference is minor and shouldn't be a concern.